whatever transistor on the board that controls it might be cooked too

Check the Pinwiki LW3 page.
The right flipper button leaf switch will make contact with the lugs of the shooter coil. Much chaos created.
Good hunting.

F5 is your 50V supply. If it's blowing instantly then a coil may still be bad but the associated transistor would have to be shorted. A shorted coil (or diode on the coil) won't blow a fuse until it's energized so one of the TIP 36C transistors on the PPB is most likely shorted.

The 50V coils and associated transistors on that game are the VUK-Q2, Laser Kick-Q3, Ball Launch-Q4 and Knocker-Q5.

Disconnect CN2 from the Solid State Flipper board and see if it still blows the 50V fuse.

I'm getting confused. You said you were blowing F5. There are two F5 fuses. One on the power supply and one on the PPB. Both of them are 5 amp Slo-Blo. Since you said disconnecting J7 stops the fuse from blowing I assumed the F5 you were talking about is the F5 on the PPB that feeds the 50V high voltage solenoids through J7. So what was the logic in changing BR2? BR2 is for the 34V low voltage solenoids and protected by the two 8 amp Slo-Blo fuses in the backbox.

J4 on the PPB is the AC into the bridge (BR1) on the PPB which feeds the 50V out J7. The 50V only goes to a few circuits so this shouldn't be that hard. If you disconnected CN2 on the Solid State Flipper board (below the playfield on the left on the left side of the cabinet) and it still blows, you've narrowed it down to the 4 coils and associated circuits I listed above. If you changed any of those coils double check to make sure the polarity is correct. The 50V (Violet-Yellow for the VUK, Laser Kick and Ball Launch or Yellow-Violet for the Knocker) goes to the cathode (stripe) side of the diode on the coils. J8 on the PPB is the return. If the fuse blows with J8 disconnected there is a ground short somewhere with those Violet-Yellow, Yellow-Violet wires. If the fuse doesn't blow with J8 disconnected but does when it's plugged in, the issue is most likely the coils, diodes or associated transistors on the PPB.

Splicing the Violet-Yellow wire the way you did is a bad idea because it can get confusing if someone's not paying attention. The regular Violet-Yellow wire is 50V and should go to the cathode (stripe) side of the coil. The Brown - Yellow should go to the anode. If those were reversed or connected together you have no doubt blown Q4 on the PPB board. If you're 100% sure you didn't have that wrong and Q4 is good then your diode and or coil is bad.

As for the MPU not booting. This is a separate problem. The only voltage that board needs to boot is 5V. Check for good 5V at the test points at the top right of the battery pack.

There is a boot up sequence indicated with those LED's on the MPU. Under normal operation the PIA and +5V lights will come on with power up. A second or so later the PIA light should go out and the Blanking LED should come on. Internal diagnostics can sometimes display a failure "blink" code displayed by the PIA. Unfortunately this is not 100% accurate but often times it's a good start. If the PIA blinks once the RAM at D5 is bad. If it blinks 3 times the EPROM at C5 is bad. If the PIA stays on solid there is a buss issue. That being said, how old are those batteries? I've seen low batteries corrupt the CMOS and cause game lock ups. Wouldn't hurt to remove the batteries and see if there is any difference in symptoms.

If we're still talking about the ball launch coil then yes the PPB (Q4 to be exact) is probably the cause. However since Q4 is turned on by the CPU it could also be an issue with the CPU. To isolate disconnect CN12 on the CPU and briefly turn on the game. If the coil still locks then Q4 on the PPB is bad. If it doesn't lock then look at Q27 on the CPU board.