It sounds like you've got an open circuit at the high voltage capacitor at C5 on the solenoid driver board. Its purpose is to filter DC ripple and store energy to raise the voltage going into the high voltage regulator circuit.

Check the back of the solenoid driver board at C5 for cracked/fractured solder joints. If solder joints are ok, replace C5.
The flickering you're seeing is the lack of C5 filtering the DC ripple.

The unregulated voltage out of a standalone rectifier board when the solenoid driver board is not connected is about 170V. In your case capacitor C5 is not working for whatever reason that you need to investigate.

Absolutely. The capacitor stores energy and brings the voltage up to what you are expecting.
Unfortunately the voltages listed on the Bally schematics are a bit all over the shop. For example, TP5 on the rectifier board is listed as 11.9VDC. You will only read this voltage when the solenoid driver board is disconnected. When you connect the solenoid driver board the large capacitor at C4 stores energy, filters a lot of the DC ripple and brings the voltage up to between 14.5 - 16.5 volts range.

So, the 11.9V voltage at TP5 is listed with respect to the solenoid driver board NOT connected.
The 230V voltage at TP1 is listed with respect to the solenoid driver board being connected.

See the waveform diagram below. The RMS readings are what your meter will read out.
The DC voltages on a standalone rectifier board are represented by the "Rectifier DC Waveform"
When you connect the solenoid driver board which applies the filter caps to the unreg HV and Logic supplies, the waveforms become "Filtered (via capacitor) DC waveform". You can see the capacitor in circuit raises the voltages.

Voltage_WaveformsC.jpg

Check that you're getting good continuity on the display latch strobe signal on pin 15 on that displays connector.
Also check that you're getting good continuity on the display blanking signal at pin 10.
Effectively check the solder joints on the pin header of that display for fractured/cracked solder joints.

But my suspicion is that the 4543 BCD decoder chip on the display board is faulty. If you have electronic freeze spray or aerosol air duster (it expels cold air) spray some on the 4543 chip to cool it down and see if the problem goes away for a few seconds.

The top segment is listed a segment "a" on the display schematic. Transistor Q13 drives that segment. Test Q13 for a short (use transistor Q14 as a reference for measurements). If Q13 is ok, suspect the 4543 BCD decoder chip. Pin 9 from the chip drives segment "a".

The common method is to use a plasma ball, see here:

https://pinside.com/pinball/forum/topic/quick-way-to-check-williams-sys3-7-display-glass#post-2456510

Put the plasma ball up against the display glass and if segments glow, the display hasn't out-gassed. Earlier in that thread is an amazon link to a plasma ball so you can see how it looks.

Cheers!