I agree - that's what I would do.

You want to avoid shorting to the same spot, so you could get a very small piece of heat shrink or strip a piece of insulation off a wire to create a small tube to wrap the leg of the transistor in. From there you could add a proper jumper wire on the reverse side of the board. Another way would be to bend the center leg out to avoid the hole altogether then running wrap wire around the transistor leg, through the hole and back to the resistor pack.

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After you did this, you still measure a continuity/low resistance to ground where you shouldn't? Did you check to see that the short was cleared after you removed the 7408 but before installing the new replacement?

It's possible to have seemingly unrelated problems be related....but not always easy to come to this conclusion. I see nothing as an obvious single point of failure for these multiple problems from the info presented. In these cases I recommend focusing on one problem at a time. Then when it is solved, sometimes other problems that are related are revealed. If you are comparing measurements between your non-working channel and a working one and the measurements differ wildly, then that is clue to be followed.

Did you check the downstream wiring by momentarily grounding Q43 tab to make sure the left scoop fires?

After that, get a DMM on the 7408 output pin and see if you get a pulse in test mode.

from the tech guides at http://techniek.flipperwinkel.nl/desega/index2.htm#trans

Testing TIP122/102 Transistor and Down-Stream Wiring/Coil.
If the coil fires in the above test, there may be a transistor problem. Next test the TIP122/102 transistors. Only do this for the TIP122 or TIP102 transistors! Damage can occur if this test is done on other transistors (like TIP42 or TIP36). This test will test everything from the CPU board down to the coil itself. If the TIP122/102 and coil pass this test, and the coil still doesn't work in game play, the problem is more "up stream". All that is left is the 2N4401 pre-driver transistor, and the logic TTL chip that ultimately controls the whole process (a 7402 for the special coils or 7408 for the constant power solenoids), and the PIA 6821 chip.

Note the TIP36c transistors can be indirectly tested using this method too, BUT the TIP122 pre-driver must be grounded. All TIP36c transistors use a TIP122/TIP102 as a pre-driver. If the metal tab on the pre-drive TIP122/TIP102 is grounded, this will activate the TIP36c, which will energize it's associated coil.

Game is on, and in diagnostic mode (push the green coin door button down, and press the black button on games Frankenstein and before to go into diagnostics mode).
Remove the backglass.
On games WWF Royal Rumble and later, close the coin door.
Find the transistor that controls the coil and/or flasher in question (refer to the manual).
Attach an alligator clip to the grounding strap in the bottom of the backbox.
Momentarily touch the other lead of the alligator clip to the metal tab on the TIP122/102 transistor (only works on these, may damage other transistors).
The coil or flasher should activate.
If the coil or flasher does not fire, it may be a transistor that is multiplexed through the L/R relay.
To energize the L/R relay (which will fire the other coil/flasher that is multiplexed), attach another alligator clip to the grounding strap in the backbox. Connect the other end of the alligator clip to the metal tab of transistor Q29. This will energize the L/R relay on the PPB or MRB board.
If the coil or flasher does not fire, and the coil or flasher did fire in the previous test, there probably is a wiring problem. A broken wire or bad connection at the connector plug would be most common. It is also possible a driver or pre-driver transistor is bad. Use the DMM meter to test the transistors on the board (see Transistors Testing Procedures for details).

Since it has not been presented earlier, I have to ask the question: Absolutely no signs of former battery corrosion on the MPU board?

Some housework. Check all coil mounted diodes. Check all driving transistors. The point is to make certain the diode protection is in place, because if you don't do this you run the potential of tracing your tail putting new parts in such as the driver transistors and having them get killed immediately. Once you know the downstream wiring, coil protection, and driving transistors are good, then you are left with working upstream into the logic circuitry.

Ok. Then the driving transistors are confirmed good and the downstream wires and coils are confirmed as good. The focus of your troubleshooting forward will be on the logic section.

Try reading through http://techniek.flipperwinkel.nl/desega/index2.htm#trans particularly the section titled "I've Done the Above Tests & they Work, but the Coil still doesn't work in Game mode."

I would go to the 7408 and gates before the coil drives and compare the signals at the inputs and outputs between a known good coil drive circuit and the bad one. You can use a logic probe, oscilloscope, or DMM to do this. Most of the time I just use a DMM set to DC volts. Put the game is test mode, and jot down the results while probing the signals, noting the states of the inputs and outputs at rest and look for the changes or spikes of a pulse to determine logic highs and lows. Once I know what is going on there, I could find out which direction th head next.

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Just look for the pulses. Put in coil test, set your probes up to monitor a pin on a known good solenoid channel so you know what you are looking for, then move the probe to an equivalent pin on a defective channel to see what happens there when the MPU calls for that solenoid to be activated.

TTL logic is cheap enough now... that if I've validated all works from the driver transistor to the coils... then I'd just shotgun the remaining TTL logic and replace them all. $0.75 - $3 for the peace of mind of not having to worry about the state of the logic.
Of course; I wouldn't do this for an unobtainum chip... just the common stuff like 74xx and 40xx series logic. Just my $0.02.

having said that: If your looking for some troubleshooting fun; by all means go for it.

Your voltmeter or digital multimeter doesn't have probes?....I don't understand.

SCR.s are for lamp circuits and transistors are for coil circuits. Fundamentally they are both used as switches in pinball, but the circuits have differences.

But you do understand the concept of divide and conquer troubleshhoting. If you are testing a device between the logic section and the drive circuit and the signal is not present, we look upstream into the "higher" logic. If the signals we desire are present, then we look downstream to examine the drive circuit.

The part is cheap enough, true. It's just a waste of time to replace a part that isn't the problem.
Shotgun is pretty much a last resort method. I'd rather take a few minutes with a meter to find what is actually broken.

What chips do you need? I have a wide variety, most likely have what you are looking for.

I used to have a bunch... i was doing a lot of board work for people for awhile. Let me check my stash tomorrow and get back to you.

It looks like solenoids 1-8 are driven by the 74LS273 but solenoids 9-16 are driven by the 6821. You didn't mention which specific solenoids do and do not work in diagnostic test. Note the switched solenoids are driven by several different 6821s.

If you replace the 74LS273 but the failing solenoids are in the 9-16 range then that won't fix them.

Based on that I agree. I would replace the 74LS273.

I've never owned a logic probe. We don't even use them at work (30+ years career digital electronics) You don't need a logic probe. You can do 90 percent or so of the logic troubleshooting with good digital multimeter.

If you have also verified the gates of the 7408 pins are behaving the same....why would you replace the 74LS273? ...signals can't jump over a bad 74LS273 and become correct at the 7408. You have replaced the 7408 and verified the pins are behaving the same, the problem must be downstream from there.

I think it's the other way around--inputs are at 12+13, output is at 11. Wayout can set the record straight for sure though.

If I'm not mistaken, the blanking signal holds one input 'high' (pin 13) while the other input (pin 12) gets switched 'high' from another chip, leading to a 'high' output (pin 11) from the 7408...

Yes, this is correct. The only condition that produces a high output at pin 11 is pin 12 and 13 high. See the truth table I posted earlier.

Switched solenoid 4 is for the center thumper bumper. It would help if I could find a solenoid table....like Williams games put in their manuaks. Switched solenoid are essentially the same as Williams special solenoids. Constant power is available to the pops, slings and some kickers that require faster response than running through CPU logic.

Actually, between the 7408 and the driver transistor. You already verified correct signals at the 7408....no?..or at least that is what I interpreted in your post.

Just checked my parts.. i have 138,164, 244, 373,374.... sorry man.

Congrats.... I find boardwork to be really relaxing and satisfying. Glad you were able to get through it.

Good work!