I'm betting on a bad power supply/connection or a loss of heatsink on the CPU, either one will present the issues you describe.
Motherboards are cheap an plentiful on fleabay...
http://www.ebay.com/sch/i.html?&_fro...%20motherboard
Honestly, you can find pretty good laptops brand new under $400, so upgrading rarely makes sense, other than adding RAM or possibly upgrading to a solid state drive.