Unfortunately, I don't expect Cogs to work with the Intel GM45 Express graphics card. It takes some relatively sophisticated vertex and fragment shaders to make all those nice reflective materials, so it won't run on older or low-end graphics cards.
I don't know if there is a difference between a GM45 Express and the "Intel(R) GM45" card Xorg tells me I have, but it works ok here (Debian sid) now that we have a 64-bit version. A little choppy, but definitely playable with shadows and post filters off. The 32-bit version caused the GPU to hang (according to dmesg), with the same symptoms Bryce reported.
$ uname -a
Linux ataxia 126.96.36.199 #1 SMP Fri Jun 17 20:07:07 EDT 2011 x86_64 GNU/Linux
$ glxinfo | grep s3tc
GL_NV_vertex_program1_1, GL_NV_vertex_program, GL_S3_s3tc,
$ grep Intel /var/log/Xorg.0.log
[ 34.486] (II) intel(0): Integrated Graphics Chipset: Intel(R) GM45
$ lspci -nn | grep VGA
00:02.0 VGA compatible controller : Intel Corporation Mobile 4 Series Chipset Integrated Graphics Controller [8086:2a42] (rev 07)
From the GPU hang, from kern.log:
Jul 31 16:07:14 ataxia kernel: [drm:i915_hangcheck_elapsed] *ERROR* Hangcheck timer elapsed... GPU hung
Jul 31 16:07:14 ataxia kernel: [drm] capturing error event; look for more information in /debug/dri/0/i915_error_state
Jul 31 16:07:14 ataxia kernel: [drm:i915_wait_request] *ERROR* i915_wait_request returns -11 (awaiting 68336 at 68315, next 68337)
Jul 31 16:07:15 ataxia kernel: [drm:i915_reset] *ERROR* Failed to reset chip.
It is techincally possible for you to install drivers to render Cogs with software emulation, but it will likely render only about 1 frame every 10 seconds.
After the GPU hang, I once managed to kill and restart X somehow or another with the GPU still hung, which led to GL using the software renderer. 1 frame every 10 seconds sounds about right. And it was extremely blurry for some reason, too.