Hmm, y'know I think it might be just the battery. I put in another one that I thought was good. The chime was louder than usual but it fired right up. Then I got the date/time is wrong error. I left it a while with no battery installed, tried again and it fired right on up too. Both times the screen kicked in faster than when I had the old battery installed.

I really need to get myself a multimeter so I can check things like this out. I'm just hoping it won't give me any grief once I put in a good battery.