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
I only work with notebooks because they are compact and portable. Having used several Dell Latitude, HP Pro, and Lenovo thinkpads (formerly owned by IBM), I must say I like thinkpads the most. Thinkpads are very reliable with good cooling mechanism, and in general more portable. I plan to get thinkpad T440p as it is the only 14" business grade notebook with a quad core CPU.