You can use an NTE949 to replace the 739 in SOME circuits. The 739 has pins for lag networks that are important for stability in some designs that the 949 does not have, you may need to restabilize the amp elsewhere if this is the case.
You (usually) need to add a 5000 ohm resistor from the output pins (one each from pins1 and 7) of the 949 to the V- pin (pin 4). You may be able to skip this in circuits where there is already a resistor there.
The AC fuse (3 amp) on the input circuit board was blown. Have fun changing it...
There were three burned traces on the output board. Two were on the foil side, and easy to see. The third was on the parts side, under a big coil (L1) where it could not be seen. To check for this, measure from pins 7 and 8 of the TDA7294 to the 8 pin cable that goes to the input board. Both should connect to one of the pins. If either one doesn't, you have a burned trace to find.
If I understand you correctly, you said the amp was fine after being stored but not fine after you opened & cleaned it, etc. So, you need to check the work you did. Cleaning the cases of the pots wasn't likely to cause any problems. Perhaps you accidently bent a part over and its shorting out to another part, or to the chassis. Do a close visual inspection. Undo any other changes you made, for instance, remove the ground you added and see if that makes any difference.
I'm not sure replacing all the pots will make a difference, lots of old pots still work great. If they are dirty, many clean up fine with a good cleaner. Use one made for use on pots and that includes a lubricant to help them last as long as possible.
If the amp lost volume while it was in storage, you might be looking for a bad capacitor. Electrolytics (like the little blue cans in your photos with a lead out of each end) especially don't age well. Neither do some old paper types, but that amp might not have any any of those, (I don't see any in the photos). Note that electrolytics have a positive and a negative end, be careful not to get them backwards.
Another possibility is that you damaged a part even though it was off while you were working on it (it was off then, I hope). Sometimes there is enough energy stored in the circuits to allow that to happen if you accidentally shorted something out moving things around. In this case, probably a transistor.
These old Silvertones can really sound quite good, and a lot of people still love them. I hope you can get it going.