The computer isn't crap. The Pentium E line is based on the same silicon of the Core 2's. It has less cache and a slower FSB, but the Pentium E is vastly superior to other Pentium 4/D's because of it's architecture.

1GB is a little on the low side for RAM, and given the low price of DDR2, you could likely bump it up to 2GB for next to nothing.

The GeForce 9600GT would be a nice bump from the Radeon HD 2400, as that particular Radeon is the low-end for the 2x00 series. Most likely you're set with a PCIe (PCI Express) x16 slot. Info here.

The only concern I have is the power supply you have in there currently. I don't know who built it, but given the low-end video card, I'd bet it's very likely not meant to run a power house rig. You'll have to crack the case open to see what the label says on the unit. If your power supply isn't up to task, you can run into things like instability all the way up to hardware damage, particularly if it's a shoddy unit.