If it's a dell (I unfortunately used to be one of their on-site techs, working for Unisys), then yes, the motherboard could possibly be failing as ardvark has suggested.
Although, it could just be the fan... Simply by pulling out the fan and spinning it with your fingers could let you know if it has seized or not. That's a simple, cheap fix that anyone can do. No sense in taking it to specialists if that's the case.
Powersupplies, are usually running or not running. Yeah, I've seen where they are starting to fail and cause weird problems, but when a transformer goes, a transformer goes. Doesn't usually take too long. I'd definitely go the fan / mobo way.