Dell Dim 4300 shutting down with touch of back

Several days ago my Dimension 4300 shut off suddenly and I couldn't seem to get it to come back on. I'd push power button and no sign of life.

I just received and installed a PC Power & Cooling Turbo-Cool 425 power supply. It came right on and I thought all was well. Then within 10 minutes I went to plug my USB from digital camera into back USB port and it immediately shut off. At first pushing power button did nothing. I moved the computer back onto a table to look further and just for grins pushed power button and it started coming on. Because I had unplugged monitor and all, I thought I'd plug them in after it appeared it had booted. The second I just touched the back of the case, it shut itself right down.

I'm wondering if the first power supply wasn't bad (though the new one it a better power supply) and that the problem is a short somewhere. The one thing I do a lot is plug USB devices in and out and wonder if something has come loosed within them and causing short. I don't see anything loose on motherboard or within computer. I replaced IDE cables a while back and put in one that has a ground wire that I didn't connect because I didn't see any obvious place to screw it to case and was told it wasn't necessary. Also put in new removable drive a while back and that has all seemed to work well.

I'm a little nervous to do too much trouble shooting as I'm concerned if there is a short I may fry a drive or something. Any advice would be appreciated!

Kay