The minimum PSU for a 4670 is something like 300-350W.
The Sapphire website recommends a 400W PSU - which is an 'average' 400W PSU while the Corsair 450VX is quite a bit better than average.
You should look at something other than a PSU issue I think.
Locking up doesn't sound like a power supply problem, I'm not sure what it is.
Phenom 9850 overclocked to 3.0Ghz
Gskill 4Gb (2x2Gb)
Sapphire 4670 512mb
DVD burner(not sure brand)
Seagate 250Gb Hard drive
Seagate 80Gb hard drive
Western Digital 80Gb hard drive
Hitatchi 80Gb hard drive
3 case fans
This all runs fine with a 380W Antec Earthwatts power supply. I've also got 2 similar systems with overclocked quads and radeon 4670's, one of them is also on a 380W Antec Earthwatts and the other a generic 400W Antec. The systems have run fine since 08 with these.
So nobody know's the minimum I need, just going to go by their experiences with a different system?
Seriously, Is it my PSU being to low power for my computer? Even without the graphics card in, my computer does lock up and freeze randomly sometimes just not as much as it did when the graphics card was in.
It used to restart if I left it when my computer locked up. But since I'm getting used to it I just hit the restart button before it can.
Tbh, I'm just thinking of saving up and building a new computer from scratch since this one has only given me problems since I build it like a year ago.
I just put your specs into newegg's PSU calculator. It reads 380W for your system, . This isn't "gospel truth", it's just a general idea. You need electrical test equipment to know anything better. Still, I agree, your PSU SHOULD work.
Keep following WR2's test suggestions. The best you can do is start eliminating components to determine the cause of the lockup.