I reckon its got a sock stuck in the cpu fan Jonny
Socks aside, sounds like mobo to me mate if its not posting & memory no effect, cpu's hardly ever go wrong in laptops tbh & desktops these days, repaired a few laptops in my time & never had to change cpu, fun job
Scan ebay for mobo/cpu, I'd go with mobo 1st, just make sure you get the right board, cause even same models have different generation boards that do differ slightly in possibly chipsets aswell, can be a minefield, but removal of existing board should show the part number you need no problem.