If it's a good quality power supply, you should be good. The average 7900 GTX requires a minimum of 350W with 22A @ 12V.
Now, if it's one of the Hewlett Packard (HP) or Enermax power supplies, then you may run into problems. They are very underpowered on the 12V rails and wont give you the power you need.
lmfao....dont worry. even an 8800gt will run on a 300 W. the "minimums" on the specs info stuff, is just to prevent total noobs from blowing up their comp. they just want to be secure.
even a GTX 285 under load only uses max 350. that 350 includes the procesor, ram and hard drive as well al though that comp is a barebone comp. you have a pentium 4 which uses quite a bit of power. im pretty sure it will work perfectly fine tho.