On my first build of this project... I had the same goofy hand-wave-symptoms. My problem was just as Daniel said, my analog input were floating. I think I have a 10K resistor on one of the pins, and 47K resistor on the others. (i just wanted to see if 47K would work). I kept the 47K's cause I figured that would limit a little more power consumption, but I'm also pulling the pin down to ground instead of up to 5v. There is no difference though in functionality, just different code.
It all works wonderfully!!! At first I thought this would be super simple. So the first day I had the Arduino mini board, I figured I'd be done that afternoon. Isn't that how it goes. 
At first I didn't realize that I needed the MAX chip, ignorant NEWB I gues. So after a week of futzing around with it and getting frustrated... I stumbled on your thread here - 3 days later got my chip, and I had communication with my computer via HyperTerminal, but no joy controlling projector.
Then on a whim, I sent a 'clear buffer' command to the projector before tring to turn it on - woohoo. It worked. I don't need to send Clear Buffer every time, just the first time. And I'm not even sure I need to do that. It seems that no matter what the first command I send, it doesn't work, but the second command and everything after works great. (without clearing buffer on projector).
Now however it seems that since the size of my code is pretty large, if I add just a bogus line of code (like create a function that doesn't ever get called, or send an extra line of serial data back to computer) then the whole thing breaks, sometimes... The LCD will work after upload, and so will my two toggle switches (sometimes) for power and input selection. But my momentary SELECT and MENU UP/DN buttons won't. If I comment out some older code, leaving the new stuff there, things will usually come back to life. I don't know if I'm hitting an invisible ceiling of max sketch size or what. I think it's just under 8000K, where the displayed max is something like 14000K.
Anyway. When you (hoffmangler) finially got your communication to work - it gave me great joy and hope that I to may get mine going. In the mean-time while my communication wasn't working to projector, I kept building my menu structure and user feedback systems. I still have a ways to go before I think it's finished. But so far so good.
Thanks