Don assume that because the Fans run that the PSU is OK..

From the discripotion you gave of what happened .. my first suspicion is damaged RAM sticks.. or a dodgy socket on the mobo.. some boards flex causing the center pins of the ram stick not to connect correctly.. esp on cheap mobos.. but have seen on the better boards.

Going back to the original symptoms..
HAve you checked the Event Logs.. any errors at all here? (you did say no BSODś I suspect not)
Have had a Video Card die completly, started off with restarts..and no event logs ..ie no BSODs. then the beast wouldn start at all.. new Video Card Later..all was well again..

Give that a Blast.. see if it helps