Check the CPU, RAM and Harddrive for proper seating, or remove and reseat them. There is also a Video daughterboard connection just in front of the Keyboard, CMOS  Battery and Synaptics  connections, which came unseated on me once  and caused similar problems. It requires firm downward pressure to reseat it, as does the CPU. It sounds like an intermittent connection somewhere, which can be the bane of a tech's existence.

How would I go about checking those things?

http://docs.us.dell.com/docs/systems/pmojav/document.htm     

This link will take you to all documents available for your Laptop; download the Service Manual. If you do not have Adobe Acrobat Reader, you will need to install it from a free download from here:

http://www.adobe.com/products/acrobat/readstep2.html

You need to remove your keyboard for starters, to access the CPU and Heatsink,also the Video Daughterboard Connection I previously referred to. The hard drive is in a Caddy which slides out of the left side after you remove 2 screws securing it from the bottom side.