I'm surprised nobody mentionned that both U4 and U3 might have been damaged by overvoltage , making the tantalum caps explode at the same time. I've seen this happen in the past and luckily simply changing the caps and regulators brought everything back to life. They are easy to test , even without any capacitors in place. You can test both +12 and -12 at J503. Pin 2 is ground Pin 3 is -12 , Pin 4 is +12 (Pin 1 is 5v).

If you removed C26, you can use its positive leg to test for DC coming out of the bridge , the value might be weird a bit if C26 is missing , but you should get something around 30-40V. You can also measure the negative side of the bridge by measuring the voltage at capacitor C47 that was removed. With the red lead on the positive side of the capacitor , you would read negative voltage , again around 30-40 probably (might be a bit lower) .

The +12v and -12v regulators might still be good , since the damage is on capacitors just before them.. I've seen it often where tantalum capacitors blow up , but damage doesn't spread much further..

The regulators cost and the caps cost next to nothing. If these are the only issues (very likely) then this board can be repaired for under 10$.

EDIT : I would change all 6 circled caps as they probably all have suffered damage, even if they some don't show.

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Yes, tantalums are effected by age just like electrolytics are. They are not as bad but could fail just like any other component. Older tantalums were more frail that today's and from what I read they often failed short, causing bigger issues. Changing those caps in the power circuit can never hurt. I don't think they are as critical as electrolytic, but if you have them on hand , change them it only takes a minute or two each and your board will have more chances of lasting another 25 years or more..

Not sure about the pause between your bongs , but 2 bongs would mean U9 , RAM 2064 fails and 3 bongs would mean U18 (Audio ROM) fails. You've changed the caps , but have you measured the voltages on board to see if all is OK ? If you pull out U18, U15 and U14 (if it's used) and power on , do you get the same bong sequence ? If you use audio roms from another machine, do you have the same symptoms ? Same bongs and still no sound ? If so , I would start to blame U9 that very well can have been damaged when your caps blew up (usually they blow up because of overvoltage) after all , C46 did blow up and it's on the 5V line, which powers all RAM / ROMS.

1 - No issues...enjoy a game.
2 - U9 RAM failure.
3 - U18 ROM failure.
4 - U15 ROM failure.
5 - U14 ROM failure.

EDIT : I imagine the pause could mean that you have error 2 AND 3 one after the other.. So both RAM and ROM might have died.