You need to do a bit of detective work, could be your graphics card is not recognized correctly try:-
dmesg|grep drm  (see if that is instructive)
glxinfo|grep vendor (record what you get)
glxinfo|grep renderer (see what you get there)

Is the following link any good to you
http://www.linuxquestions.org/questions/linux-laptop-netbook-25/ati-mobility-rad...
It might be informative, but also slightly out of date. I would be surprised if there wasn't a solution, but it may be complicated (I generally compile my own kernels and I'm pretty sure your card is supported in recent kernels).

I trust it is not a 32 bit version vs 64 bit processor problem is it

I am not 100% sure on this but this what I think you might hoped to have seen.
But I think the vendor string Mesa indicates software rather than hardware opengl (I know it sounds daft) if you run glxgears, you might find it renders but runs relatively slowly.

server glx vendor string: SGI
client glx vendor string: SGI
OpenGL vendor string: Tungsten Graphics, Inc. (is what you want to see at least in my case)

LINUX newbies please ignore following (I will not be responsible!!!)
I would be tempted to recompile the kernel but that is probably not necessary.
What you need to do is to make sure that the hardware driver is  picked up. Since grub2, if you want to send commands to kernel the file you need to change is /etc/default/grub.
Here is the appropriate entry from my grub config

GRUB_CMDLINE_LINUX_DEFAULT="quiet splash radeon.modeset=1"

Where I turn the kernel modesetting on (experimental)
after changing this file you need to run 'update-grub' afterwards to update
/boot/grub/grub.cfg (which is the real kernel config file)
In my case turning modesetting on has no effect because it is the default for my custom kernel, you however may need to disable framebuffer driver for example.

I hope that helps because it is difficult to cover all the bases.
However you can also try the drivers from radeon
http://support.amd.com/us/gpudownload/Pages/index.aspx
Going that route does means compiling the kernel modules on your own machine, in this case you probably should prefer the distro kernel source/headers (or at least in the first instance).  I have found a community wiki that seems have some relevant information re installing latest drivers from ATI http://wiki.cchtml.com/index.php/Ubuntu which suggests that headers should now be sufficient.
PS if you do decide to compile a kernel, the latest stable is 2.6.33.2 from http://www.kernel.org/, and there are ongoing developments for graphics drivers I would also recommend doing it the debian way; for slightly outdated instructions (pre grub2 also predates relatively recent gcc support for the 'march=native'  CFLAG which detects machine specific optimizations)  follow link:-
http://www.howtoforge.com/kernel_compilation_debian_etch