The IGP (or Integrated Graphics Processors) are pretty brain dead cards.
They are used by OEM's to offer low cost but still somewhat 3D capable devices, usually for Laptops but rarely on Desktop units.
The ATI offerings run the gamut.
Almost all utilize a "shared memory scheme" (phew!) so the total amount of RAM available, the speed of the processor and the amount of shared ram that you've allocated to video, have huge effects.
HL2 will run on these cards, with many effects turned OFF by default. That is HL2 itself detects the capabilities of the device and disables those enhancements which the IGP chips do not support. In spite, or because of this, you can still get decent frame rates out of HL2 on a laptop provided the rest of the equipment is up to snuff. However particle effects, specular lights, etc. go away, which many people don't notice.
Now all of that said, people here report being able to run G3 on the 320m just fine... so some suggestions:
a) Increase the amount of RAM allocated to video to the MAXIMUM your machine supports.
b) Because this RAM is borrowed from main memory, having 512megs or MORE is a must!
c) A fast processor is helpful.
d) If G3 is throwing errors, you may have vestiges of OEM or older ATI drivers laying around which will cause conflicts.
Try Googling for the "Nasty File Remover". Grab and install it.
Download the LATEST drivers for your ATI board.
AVOID THOSE FROM THE MANUFACTURER OF YOUR LAPTOP!!!!
These are usually way out of date.
Check out places like laptopvideo2go.com, etc. for "patches" to the latest drivers, to get them to install on your laptop if needed.
Once you have the latest drivers ready to go...
Uninstall your existing drivers and reboot your system (it will come up in VGA mode).
Terminate any attempts to re-install the vide drivers, and run the "Nasty File Remover" to delete any ATI video drivers, infs, etc. you may have laying around.
Run the Directx9c redistributable file (yes again, just in case) and then install the updated drivers.
Reboot and try again.
Usually if programs such as HL2 will run on your machine, so will G3.