Your power supply should have enough power to keep your system running, if it was sufficient before, since E6600 is very energy efficient. The only issue that I think you may have (I ran into this with my Enermax 460) is that the new Core 2 complient boards use 24pin power plug + a 4 pin connector that the P4's used, while the 478 based motherboards (865, 875) used a 20 pin connector. If you have a 24pin, then you should be fine. If not... I saw online adapters that converted PSU-20 pin to 24-Motherboard pin, though most of them do it in the opposite direction PSU-24 to 20-motehrboard, and given that they use the same rails for stuff, I dont see why that wouldnt work. But that's my theory, I did not test it.
I got a new power supply because my enermax wasn't enough for all my hard drives, and I am tired of having a second power supply hanging outside my case connected to several hard drives 🙂