Playing by the odds, its best to double-check your circuitry first, literally. Its very easy to get so close to a circuit that when checking it, assumptions leap-frog past dutiful checking. I've found that checking it in reverse order to disrupt assumptions helps. If I check it again, I use a different sequence, a helpful technique of disrupting what one expects to find.
You might want to add a few LEDs with the spare gates so you can give your self some feedback in the firmware. Maybe its enough to have the serial port converted to RS232 on the prototype board and feed it back to the PC for messages from the firmware.
If you have the tools, you might write an application program on the PC to interface with the board. Do a loopback and such before throwing the Hail-Mary pass to find out if it all works perfectly in MIDI first try.
One mistake I see a lot in electronic hobby advice boards is someone suggesting the first thing to do is replace a chip... buy another and see if it works. BAD ADVICE. If a board is wire-wrapped or breadboarded, the odds a heavily favoring a mistake there just in the hand assembly of the board. Replacing chips or "Shot-gunning" as its called, should only be a quick attempt if you're dealing with a production board that has apparently been tested out and proven by at least the number that have been sold. Only if a product has been on the market and sold enough, can you really assume its likely not the board or the assembly. Of course such pristine circuitry can not be assumed in wire-wrapped or breadboarded prototypes; if the connections are all correct, you could have a bad wire, a bad wire-wrap contact or other insidious little bugs to find with deduction and inspection.