I have an old Pavilion Slimline with a Pentium Dual Core E2140, 2GB RAM and a Radeon HD2350 graphics card. I thought about giving new life to this machine with Linux.
At first I tried Elementary OS and directly installed it thinking it couldn't be performing worst than Windows, but I was wrong. The problem was clear: graphics card not being used properly. System speed was not unbareable, but the machine was generally unusable. A lot of sceen tearing, big problems in scrolling menus and browser pages, impossibility to watch video, sloppiness in moving and resizing windows.
Now I'm trying Xubuntu and Lubuntu live from USB, and they are even better in general system speed, but graphics problems are still there. The system is always able to properly recognize and name my card, so I don't think it's using generic drivers, software rendering or something. And if I go into Additional Drivers it gives me no third party drivers to install, so I really don't know what to possibly do to get an enjoyable desktop experience on this machine.
I find it really strange performance is THAT bad, I've always had excellent experiences with Linux on older hardware.
UPDATE: I found out that old 12.6 fglrx drivers works on my card on 12.04.1 or previous versions. So I installed Xubuntu 12.04.1 and got fglrx to work, but I still have bad performance. According to fglrxinfo command proprietary drivers seem to be working, so I can't really see what's the problem. Maybe this is the least linux-friendly graphics card in graphics card history and there's nothing that I can do other than binning this machine. :|