I've the same problem with a Lenovo Thinkpad Z61p and ATI M56GL [Mobility FireGL V5200] on Ubuntu 12.04. I'm not able to use the proprietary driver, because the support for this chipset was abandoned years ago. So I've to use the radeon driver. 

Here is some info:
> lspci
    01:00.0 VGA compatible controller: Advanced Micro Devices [AMD] nee ATI M56GL [Mobility FireGL V5200]

> lsmod 
    radeon                729591  1 
    ttm                    65344  1 radeon
    drm_kms_helper         45466  1 radeon
    drm                   197692  4 radeon,ttm,drm_kms_helper
    i2c_algo_bit           13199  1 radeon

> Xorg.log
...
[    20.538] (II) Loading extension DRI2
[    20.538] (II) LoadModule: "glx"
[    20.539] (II) Loading /usr/lib/xorg/modules/extensions/libglx.so
[    20.539] (II) Module glx: vendor="X.Org Foundation"
[    20.539]    compiled for 1.11.3, module version = 1.0.0
[    20.539]    ABI class: X.Org Server Extension, version 6.0
[    20.539] (==) AIGLX enabled
[    20.539] (II) Loading extension GLX
[    20.539] (II) LoadModule: "dri"
[    20.539] (II) Loading /usr/lib/xorg/modules/extensions/libdri.so
[    20.539] (II) Module dri: vendor="X.Org Foundation"
[    20.539]    compiled for 1.11.3, module version = 1.0.0
[    20.539]    ABI class: X.Org Server Extension, version 6.0
[    20.539] (II) Loading extension XFree86-DRI
...
[    20.548] (II) RADEON(0): [dri] Found DRI library version 1.3.0 and kernel module version 1.33.0
...
[    21.062] (II) RADEON(0): [DRI] installation complete
...
[    21.080] (WW) RADEON(0): DRI init changed memory map, adjusting ...
[    21.080] (WW) RADEON(0):   MC_FB_LOCATION  was: 0xdfffd000 is: 0xdfffd000
[    21.080] (WW) RADEON(0):   MC_AGP_LOCATION was: 0x003f0000 is: 0xffffffc0
[    21.080] (II) RADEON(0): RADEONRestoreMemMapRegisters() : 
...
[    21.539] (II) AIGLX: Screen 0 is not DRI2 capable
[    21.539] drmOpenDevice: node name is /dev/dri/card0
[    21.539] drmOpenDevice: open result is 12, (OK)
[    21.539] drmOpenByBusid: Searching for BusID pci:0000:01:00.0
[    21.539] drmOpenDevice: node name is /dev/dri/card0
[    21.539] drmOpenDevice: open result is 12, (OK)
[    21.539] drmOpenByBusid: drmOpenMinor returns 12
[    21.539] drmOpenByBusid: Interface 1.4 failed, trying 1.1
[    21.539] drmOpenByBusid: drmGetBusid reports pci:0000:01:00.0
[    21.551] (EE) AIGLX error: r300 does not export required DRI extension
[    21.551] (EE) AIGLX: reverting to software rendering
...

So I've direct rendering:
> glxinfo | grep -i render
        direct rendering: Yes
        OpenGL renderer string: Gallium 0.4 on llvmpipe (LLVM 0x300)
            GL_NV_conditional_render, GL_AMD_draw_buffers_blend,

..., but it is software-rendering:
> /usr/lib/nux/unity_support_test -p
    OpenGL vendor string:   VMware, Inc.
    OpenGL renderer string: Gallium 0.4 on llvmpipe (LLVM 0x300)
    OpenGL version string:  2.1 Mesa 8.0.2
    
    Not software rendered:    no
    Not blacklisted:          yes
    GLX fbconfig:             yes
    GLX texture from pixmap:  yes
    GL npot or rect textures: yes
    GL vertex program:        yes
    GL fragment program:      yes
    GL vertex buffer object:  yes
    GL framebuffer object:    yes
    GL version is 1.4+:       yes
    
    Unity 3D supported:       no

... so Unity 3D ist not supported

-----

With the workaround from Carl I replaced all installed Mesa-Packages with:
    libgl1-mesa-dev     7.11-0ubuntu3.2
    libgl1-mesa-dri     7.11-0ubuntu3.2
    libgl1-mesa-glx     7.11-0ubuntu3.2
    libglapi-mesa       7.11-0ubuntu3.2
    libglu1-mesa        7.11-0ubuntu3.2
    libglu1-mesa-dev    7.11-0ubuntu3.2
    mesa-common-dev     7.11-0ubuntu3.2
    mesa-utils          7.0.3~rc2-1ubuntu3

and configured the module in /etc/modprobe.d/radeon-kms.conf with:
    options radeon modeset=0

With a worse result:
[    19.912] (II) AIGLX: Screen 0 is not DRI2 capable
[    19.912] drmOpenDevice: node name is /dev/dri/card0
[    19.912] drmOpenDevice: open result is 12, (OK)
[    19.912] drmOpenByBusid: Searching for BusID pci:0000:01:00.0
[    19.912] drmOpenDevice: node name is /dev/dri/card0
[    19.912] drmOpenDevice: open result is 12, (OK)
[    19.912] drmOpenByBusid: drmOpenMinor returns 12
[    19.912] drmOpenByBusid: Interface 1.4 failed, trying 1.1
[    19.912] drmOpenByBusid: drmGetBusid reports pci:0000:01:00.0
[    20.422] (EE) AIGLX error: Calling driver entry point failed
[    20.440] (EE) AIGLX: reverting to software rendering
[    20.441] (EE) AIGLX error: swrast does not export required DRI extension
[    20.441] (EE) GLX: could not load software renderer
[    20.441] (II) GLX: no usable GL providers found for screen 0

I've no OpenGL at all.