If you do get some sound, then I suspect the cards are making intermittent contact.

The card edge connectors need to be really clean, bright gold, and you need to spray plenty of deoxit on the backplane connectors and agitate using a toothbrush.
Each card needs to be cleaned on both sides and you may need to insert and pull out a few times for really good contact.

The digital output card looks to have been very poorly repaired with cheap capacitors, although if you're not using the analogue outputs on the card, I wouldn't worry too much about it.

Check that the PSU is outputting +5.1 volts on the red wires - there should be a trim potentiometer in the PSU that can adjust the voltage - be careful though! - 5.0v is too little, 5.2v is too much!!
Ideally, the voltage should be measured from the regulator on the comms board (top, middle board)

Have a read of Meridian's TN32 - Repairing a G68 following a PSU failure - that should help.

Remember faulty cards can pull the entire bus down and prevent the entire unit working, start with a basic configuration (as per TN32) and build up slowly.

Good luck,

Steve