Your suspicion is correct..It's the PSU.
Get a 750-850w with a single 12v rail.
Thermaltake tr2,Lepa,Enermax,Kingwin(higher-end ones)..Rosewill,Seasonic,Silverstone.
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148517 or
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148557
kit: http://www.newegg.com/Product/Product.aspx?Item=N82E16820148560
That's a very old,junky platform.
The 1st phenoms were pretty bad as well.
I don't see where you're from..If it's US;There are much better options.
You want Gddr5 and 256-bit bus for a GPU to be a good one..
I'd say new CPU+GPU ..