Upgrading from a 7950 GT to a XFX 4770?

massive difference... you will be pleased with the upgrade
speak from personal experience, upgraded from 7950gt to 4850 a while back

Could you post your computer specs as well?
And the 4770 should be a pretty good upgrade from that 7950 GT

Would be glad to.

However, I can give kinda basic specs from what I know, but I'm assuming there is a program I can use to quickly scan my computer and grab the specs. Can you suggest one?

Well just basic would be fine, only needed ones are CPU and Ram basically, just to see if you would meet any piping issues, although it isnt very likely

4GB of ram and a dual core 2.41GHz processor.

Then yes you can easily make it into a 4770 which should offer a good performance boost from the 7950, mainly just because the 7950 is older, the 4XXX series of ATI was made to combat Nvidia's 9XXX series, and some of the lower 2XX series of Nvidia

I myself have a XFX Radeon HD 4770, and is probably one of the best price/perf cards there are. I can max out all the games I play. I'm supposing your power supply should be ok, considering that both the 7950GT and HD 4770 need just one six-pin PCI-e connector.

Oh yah forgot to ask what your power supply was...it probably shouldnt be a problem but it could be... So if you know your PSU spill it then! lol

Lower end 2XX series is GT 220, GT 240, GTS 250, the GTS 250 = 9800GTX+ while the GT 240 is less than a 9600GT.

We most likely don't need to know you PSU, as the 7950GT needs more power than a 4770, so other than capacitor aging there shouldn't be a reason.

The G71 except for the GTX boards use less than 75w at stock clocks (61w) so when it comes to power you wont notice that much of a difference in consumption. Performance how ever you won't be disappointed to say the least. I have had 3 7900gs ko boards as well a 7800gs (G71) they did fairly well except the shader was just far to weak as well the low clocks added to the suffering when playing crysis. I still got 2 7900GTX Duo's which are monster cards (size) look at my avatar in the middle that is it.