If you installed ATIs driver, it probably overwrote Mesa's version of libGL.so, which breaks radeon and radeonhd. You need to reinstall mesa's drivers to compensate.

$ apt-file find /usr/lib/libGL.so

And one of those will need to be purged and reinstalled.

# dpkg --purge --force-all libgl1-mesa-dev libgl1-mesa-glx
# apt-get install libgl1-mesa-dev libgl1-mesa-glx

And restart X. In otherwords, radeon and radeonhd do work. In a favorable wind.

$ dpkg -l '*-mesa-*'

To see what might be installed with relation to mesa. mesa3d.org

Well, since the 2 radeon-drivers doesn't work on that computer even after a fresh install I find it best to use ATI:s driver.
Also I find ATI:s driver to be better really, on my 'puter I switched from radeonhd to ATI:s because 3D was no good.

The Radeon and RadeonHD devs think the driver works with your card - better tell them the bad news.

There is usually a binary package for the fglrx driver for your distro which will install without breaking your system. The only time you need the ati installer is for the absolute latest cards.

Beyond that - thread is marked solved. No worries - so long as it works.

I would have to test it more thoroughly - after all, I have had trouble with Mint & Ubuntu on other 'puters as well, that's why I recommend pure Debian even to a "newbie".
And on the Debian-system, as mentioned earlier, I messed it up by not checking what was already installed.
So it is possible that the radeon-drivers work on a "normal" system, I'm not messing with daughters computer more now that it works.