I would start by looking at the obvious, open case and power it on, does the cpu fan run ? if yes then when is last time you changed the thermal paste between cpu and heat sink... those are the two obvious things I can think of.
first one is free and easy if the fan start, then c low some air when computer off and clean out the fans of the heatsink.
second is cheap $4-7, get a new tube of thermal paste , take heatsink apart and clean both sides, apply a small but of paste in middle gently but firmly press down wiggling it a bit to spread paste underneath it, secure, boot to see.