I've used a PCI-E Powercolor 4650 and a Sapphire 4550. Cards above the X800 level or with uncommon chipsets may not be so straightforward in the more recent, still supported, distros that we're "shepherded" into....
1. Here's what I would do--just run the disk at first. If you can get the distro on your hard drive but video doesn't work on reboot, try using step 2. Otherwise, set your bios for 'optimized' defaults, change the boot sequence again, and then boot the live disk and set the video for safe mode in the live disk menu. Install the distro (I use ubuntu). After the distro is installed, if video doesn't boot immediately, give it a couple minutes (one of my ATi cards (a 9800XL on this machine) takes a while to boot--giving messages like "no video," "video resolution unsupported," etc., but, it does boot well in the end.
2. Failing that, you need to get "fglrx" (ATi's most current proprietary driver) on board. Reboot, get into grub with the "escape" key, and, choose the "recovery" version of ubuntu/distro, and choose "command prompt with networking." Type "Su" with master password in alternate distros and "aticonfig --initial", or "Sudo aticonfig --initial" with your user password in ubuntu. This installs fglrx from Ati's site. If you know aticonfig, you may configure your video setup well in it--otherwise, use your GUI and your distro's version of fglrx, or, possibly the terminal window and "aticonfig --initial" for ATi's most current version. You will very likely need to get fglrx on board to gain any functionality with a card of that level, anyway.
3. It's not just the video card--the monitor/card setup may not be supported. If it is, the monitor likely is compatible only to a limited extent (my monitor icon in the top right-corner toolbar of any of my ATi systems has a "slash" through it--this indicates use of a limited generic monitor driver which allows resolution switching and, perhaps, frequency switching only). Currently, I'm having trouble with my AOC 15.6" monitor and getting ubuntu to boot on that Windows system with a my Sapphire AGP 3850....
I'm very interested in purchasing the 4770 with a socket am2 board, chip, and mem someday and in finding out how this works out. Given that (probably) no one has said it's completely incompatible (i.e., a "paperweight"), this chipset likely is at least somewhat compatible. I desire to hear how this turns out and to offer any reasonable assistance possible!