When I mentioned that cooling the CPU and GPU could make more power, I was referring to overclocking...the cooling of the CPU and GPU wouldn't be the overclock; it would just allow the system to keep running while overclocked without overheating.
It sounds like the unit you are working on has a damaged thermal diode or thermal diode reading chip, and possibly missing thermal pads for the southbridge or the ram. When any of these parts overheats, digital logic can be victimized...so something simple like loading the XMB might still work, while something requiring exact logic such as verifying a key will go wrong.
I saw something similar on my own 40GB model a while back...it seems that the ram was overheating in that case. I could launch games and they would start OK, but after 1-2 minutes, everything would start to slow down (a bit like blowing up 10 cars at once in GTA4, except that the problem stayed and kept getting worse until the system froze completely). I fixed this by putting real heatsinks on the memory chips, and it never came back.
For your second question, almost any IC can theoretically cause a YLOD if it fails in the right way...it is just that the solder balls below the RSX are the most common cause, followed closely by the solder balls below the CELL...those probably account for about 95% or more of all YLODs. The other day I bought a dead PS3 Slim off ebay with a non-yellow-light-YLOD...and the problem turned out to be the southbridge.