You should be able to access the memory modules on the back of your Laptop without having to disassemble the whole thing. It's usually located behind a small panel at the bottom of your Laptop. You will probably need a couple of jewelers screwdrivers to remove the screws.
Get a copy of Memtest86+ ( http://www.memtest86.com/ ) and run it for awhile (overnight) to see if your memory is failing. If the test fails there's a really good chance that you need to replace at least one memory module.