Ubuntu 11.10 was the last release that I could install on my Dell Inspiron 1564, with this graphics card:
02:00.0 VGA compatible controller: Advanced Micro Devices [AMD] nee ATI RV710/M92 [Mobility Radeon HD 4330/4350/4550]
All releases after 11.10 froze once in 2-3 days, with color stripes on the screen. ATI's proprietary driver fglrx does not anymore support this graphics card, and xserver-xorg-video-radeon is seemingly buggy. 13.04 was worse, it froze already at the login screen. The 'solution' was to remove xserver-xorg-video-radeon, so that the system falls back to vesa, I believe.

This is already my second notebook with an ATI graphics card, with the same fate (i.e. I can not upgrade the op.system due to problems with the graphics driver xserver-xorg-video-radeon).

If there is a known workaround, or if there is any way I can feed back useful information, let me know. Otherwise I will go like this, and not buy a computer with an ATI graphics card again.

BTW the vesa driver is 95% satisfactory (I am using my notebook for work, and not to see fancy window effects). It could output video to HDMI - but I think for this you need to boot your machine with the HDMI already plugged in. When I just tried to plug in the cable when the system was already running, it did not recognize this. The only thing I am lacking is the 'present windows' feature of kde.