I agree, get the HD4770.
You MAY have some issues with your power supply. Considering you won't notice a difference with more than 4GB of RAM you should take some out and leave only a 2x2GB configuration. I don't understand how you could have 7GB anyway as it should be paired.
Taking out the RAM (that you won't utilize) will lessen the load slightly on the PSU too.
Here's the steps:
RAM
1. Turn off the computer but leave the power cord intact (to ground it)
2. read your manual's section on RAM placement
3. Ensure that you have 2x2GB of RAM in the correct slots and remove the rest
3. Turn on the computer and make sure everything works
Video Card:
1. Go to Add/Remove programs and remove your video card drivers
2. Turn off the computer, leave the cord intact
3. Inspect that you have the proper power connector (If not you'll need an adapter like a MOLEX-> 6-pin).
4. Install the video card
5. Turn on the computer and enter the BIOS (usually DEL key)
6. Ensure the graphics card order selects the PCIe first and NOT the onboard graphics
7. Reboot
8. Ignore any popup windows, download and install the latest drivers for your Operating System and install them
9. Reboot and everything should work.
FYI, they have tested extensively and the HD5870 (the newest and fastest single GPU graphics card) ran at only a hit of 1 or 2% when running in a PCIe x8 v2.0 which is equivalent to a PCIe x16 v1.0. In other words, you'd have to get a faster card then it to max out your graphics card slot so the HD4770 will not be bandwidth limited in the slightest.