I got up today, had my coffee break usual, and looked up this topic that I started. I went to do as you suggested Stuart, but my multimeter decided to croak somehow. (yes the battery was still good) Cheap-o unit anyway. I went ahead and turned it on without the keyboard; lo and behold it had no issues that I could tell. I.E., no more repeating semicolon. I did figure out that the cable that was soldered to the keyboard was brittle and was causing bad connections. I reached over and took the keyboard connector off of my parts board, soldered it in place, and used a short IDE cable I had laying around (same position on both ends) and tried it again. Almost everything worked...
After referring to the grid diagram I found for the keyboard, it seems pin 5 has a problem. The system is slow to boot into TI Basic with the keyboard connected, but with it still powered on, I can disconnect said keyboard and it moves along like it should. After I got a flashing cursor to start typing, I reconnected the keyboard and the flashing stops. I can type the command "call clear" and that works fine. I tried to type in the obligatory "Hello World" program and once I pressed the "N" key, I heard the lower tone error beep and it just freezes. I disconnected the keyboard again and the cursor starts flashing again like normal. I did try using just a jumper wire to make the "N" type up by shorting pin 5 to pin 9, but no dice. I tried any key assigned to pin 5 with my jumper wire and nothing worked. I'm soooo close to having a working TI-99....
At this point, it looks like I'll have to wait a couple days for my new multimeter to come in and go from there.