Transformer appears ok from your measurements. C.T. means "center tapped". You measured that ok, 9.7VAC to either white for each half of the center tapped secondary, then across end to end of that secondary winding is 2 X 9.7VAC= 19.4 (roughly the total 20VAC you measured) - so that is ok. That 20VAC needs to be making it over to the power supply board

The transformer appears o.k., so your problems are elsewhere. To check the controlled lamps voltage, measure DC across the violet and black wires of C61 big cap. Should be roughly 15VDC. You need to check the power supply board +5VDC. Fuse F5 gets the 20VAC from the transformer.

F2 fuse is for the solenoids, so you have some problem taking out F2 fuse, usually a sticking on solenoid either because of a switch or maybe a shorted transistor. I'd leave the solenoid fuse out and work on what might be going on with the game not booting, starting with checking the +5VDC logic voltage.

Have you seen any battery corrosion on the board? Perhaps post some clear pics of this area to look at.

Sounds like blanking might be shutting things down when those displays come up. A host of possibilities. Is the power correct and stable every time the game is powered up - such as measured directly off a Vcc pin (take measurement off any of the ROMs, pin24) Is the crystal oscillator running every time and at the correct frequency?...Clock IC after that. Almost any IC on the board could be drawing too much current, overheating from aging and suppressing power up. A bad PIA can cause a similar effect...sometimes this can be located by your sense of touch. If one of them is getting hot enough to burn your finger compared to others that may be just warm. I'm just throwing suggestions out there.

I'm leaning toward some type of instability of CPU, just from reading the previous comment. Possibly something that requires more advanced troubleshooting. The things you have indicated do not really show any red flags for the transformer, and probably not the power supply, if 4.9VDC is actually getting to the ICs on the CPU.

Power seems ok. Did you repin the connectors? Hard to tell from the pics. Measuring the oscillator requires a frequency counter or oscilloscope.

The frequency input on the GM328 should be on the back of the board: Depending on the speed of the micro on your GM328 it may or may not be fast enough to measure what you're looking at but give it a try.

GM328_FreqInput.jpg

There are no test pins for oscillator CR1 (in pic below it is the silver metal can) you need to take the measurement at the part. Since the pins are not accessible when the board is installed, you can also measure the part between ground and pin 2 of IC5. The frequency should be stamped on the part, I think it is 3.579545 Mhz. I don't think the GM328 will measure it though, as the highest spec I can find on it is 2 MHZ. Measure with the game power on. If no oscillation frequency is measured, it is fluctuating strongly with time, or it is at a different to the stated value, then the crystal oscillator is likely to be faulty.
Screenshot at 2018-11-23 03-46-13 (resized).png

Following from @wayout440, looking at the schematics TP6 is the clock out from the 6808 CPU which is the crystal frequency in divided by 4 - i.e. you should measure around 900kHz at TP6 to know the CPU is buffering / oscillating the crystal and getting a clock in.

Most likely there were some contiaminants, resisdue, or oxidation on the socket pins, possibly from the previous corrosion. Yes, the diagnostic blinking LED is a good indicator that the CPU is running. Your earlier post said sometimes you have it, sometimes the LED is not on and blinking. So is it actually fixed?....maybe. Repeated power on cycles and changes in temperature or game vibration could cause the intermittent to resurface again. If the crystal wasn't oscillating at all you wouldn't get that far - so not so important at the moment.

The MPU board will not boot without the driver board connected. Has the MPU to driver board connector been rebuilt? That is a huge trouble source for this series ofof Williams games.