Work from the bottom up, barebones, the system will (should at least into bios) boot with the core components, if problems are still present it's isolated to one of those things (testing outside the case is something to test for still).
For CPU cleaning, outside of just buying some isopropyl alcohol, i'd suggest (because it will last your years anyway), some Arctic Silver ArctiClean (kit of two bottles, it's affordable enough). Think i've gone through 2 kits in many years and it does a cracking job for CPU cleaning (i'm not being sponsored), though i'ved used it on GPU cores and other things to.
For CPU cleaning, outside of just buying some isopropyl alcohol, i'd suggest (because it will last your years anyway), some Arctic Silver ArctiClean (kit of two bottles, it's affordable enough). Think i've gone through 2 kits in many years and it does a cracking job for CPU cleaning (i'm not being sponsored), though i'ved used it on GPU cores and other things to.