I thought my computer was going kaput because it kept turning off. Turns out that some reason it's become very sensitive to movement and my baby has been using it as a prop to stand up. She moves the computer slightly and it shuts off.
Sounds like you have two options
Option #1
Good cleaning: unplug, vacuum case and fans, deep clean with can of compressed air, re-seat all connections: Memory, Video cards, etc.
Option #2
Isolate computer from Baby