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Those things aren't going to work anyway, even if you managed to get them on a 5v power supply, as they really need a minimum 2v to register a Hi input. If your 74LS00 are SOIC or TSSOP, you could just swap them over to some 74LVC00 that will work on 1.8v. If they are DIP, I'd either make another board or some small adapter board to go from the SOIC to DIP.
@ Ch3ck3rM0n - It's an FFC connector, 0.5mm pitch. https://www.digikey.com/en/products/detail/kyocera-avx/046244406010846/10313211@ John_1222 - Can't tell at all how bad the damage is from my image of the board. Clean off the leftovers of the SMT Cap and just lave it blank, it's not needed. Use some small thin wire and reconnect the traces. You can jumper wire from that spot to the bottom of the other POT lead on that stick to get the power run back to it so the trace repair doesn't have to also handle that.
It has a different footprint, also, the other Mic connector on your board there is on backwards.