Well, if physical movement causes crashes, that is a telltale sign of something not being seated firmly--which means there may not be anything defective at all, you just need to reseat the offending part. I'd definitely start with the RAM.
Look here to see where the RAM modules are located:
http://www.insidemylaptop.com/images/Gateway-NV-disassembly/fix-gateway-power-jack-03.jpg
You're lucky, both modules are accessible from the underside, so you should only have to remove 1 or 2 screws to get at 'em.
First, try removing and reinserting both modules, then try to reproduce the crash. If it doesn't crash anymore, you're good! If it still crashes, try swapping out one of the modules. You probably need to keep one module in the bottom slot. Fire it up, see if things work. If you still crash, pull out that module and put the other one in. If it stops crashing when you have one of the modules inserted, you know the other one is bad!
If you do all this and you're still having issues with kinetically-induced crashes, you may have an unseated CPU or video card, which means you'll have to remove the keyboard and poke around inside the case. (You have a Radeon Mobility card, and I believe those are actually distinct cards, not integrated to the motherboard. I had an HP once with a Radeon Mobility that got unseated. Caused random crashes and was a huge pain in the ass.)