What CPU should I get?

6670 is the very bottom of gaming gpu's. The i3 can handle much better GPU's but you will also need to upgrade your power supply at the same time. A quality 450-500w PSU would be able to power almost and single GPU made.

The i5-2400 should run fine on a 300w PSU.

While the Radeon HD 6670 is not a great graphics card for games, it should do a decent job in most games that are not overly grueling on a GPU (like Metro 2033). Even playing games at 1920 x 1080 with medium settings should give decent results. Of course, a hardcore gamer would simply laugh at the idea of playing any game at any resolution with a Radeon HD 6670 to be a joke. But not everyone is a hardcore gamer.

Actually adding onto what you said, I would agree the HD6670 is actually a decent card. My brother used an HD4670 for a few months and I was shocked at the titles it could play.

You should all know that I use a lowly 1080x768 monitor, so CPU power is my issue, not graphical power.

Your answer surprised me the most; even taking into account that this is a dell prebuilt computer, meaning the PSU is probably pretty low quality stuff, you still think such a low-end PSU could power an quad core PSU AND a graphics card?

My wishful thinking makes me want to believe you. This would save me a lot of money and hassle if I all have to do is buy a new CPU. However, how badly would a low-end card like my 6670 bottlelneck the i5-2400. Does bottlenecking create lag in it's own right, or damage the computer in any way?

Lastly, if all I upgrade is the CPU, should I be picking something besides the i5-2400? What about a i7?

Should I take it that Graphics cards use a lot more power than CPUs?

I also like to think of myself as a hardcore gamer, a hardcore gamer on a budget..

I am glad everybody has been so helpful..this has been answered to death, but:

A cheap 300w PSU can safely power a i5-2400 AND a ATI 6670??

Also, I didn't realize the 3rd gen intel cpu came out:

Intel Core i5 3450S Boxed 2.8GHz Low Power 3rd Generation Processor Form

How would this compare to the i5 2400, how much less power would it use?

Best answer selected by boorego.