trouble ...mess ...restart... screen goes blank ...Application failed to initialize... it'll just lock up... Do you think there's a general problem here? Is there something in my system that could cause most of these glitches?

Sounds like you've got a hardware problem (CPU, motherboard, or, most likely, RAM). Try booting a memtest86 floppy and leaving it going for a while. http://www.memtest86.com

Also try making sure everything (especially RAM) is seated properly. If all else fails, try underclocking the FSB/RAM. If underclocking makes it all work fine, it's fairly certain there's a hardware problem.

Peter