I checked with somebody at the place which sells PSUs etc to see what they had in stock and he agreed that 313W or 380W is a bit under spec for video editing. He suggested I try an ANTEC “high current gamer” 620W PSU as it will keep a constant current supply to the graphics card.
By the way, this computer has a dedicated 1 GB Nvidia GT 430 graphics card – this guy said that it is pretty mcuh bottom of the line for video editing, so that Antec PSU should help it a bit.
He suggested to replace the PSU first and if there are still problems to change out the graphics card for something better.