I haven't been able to find this exact problem anywhere else.

The problem with my screen is that the top row of pixels is just tiled down the entire screen. Everything on the device seems functional, I think, it turns on and off fine, if I press where the web shortcut should be on the left bar, I get another huge white box, but obviously the device isn't usable.

I'm fairly certain that the only solution would be to reset the device and reinstall everything, but without a working display or a reset button I can't really do anything. So, my question is, how can I reset without a display?

Hook it up to my computer and try reinstalling the OS2006, so it deletes everything off of the device?

Take the battery out for an extended period of time?

Or hold out hope that this is some common error with an easy fix?

This sounds a lot like the infamous white screen of death (WSOD) some 770s suffer from. There's no fix but to send the unit to Nokia for repair. It's a hardware fault.