http://www.intel.com/support/graphic...915g/index.htm
It would seem to be an Intel GMA900 (Graphics/Media Accelerator) onboard.
An oddity which DOES support Pixel shader 2.0
But does not have support for hardware transform & lighting
http://www.intel.com/support/graphics/sb/CS-011910.htm - this IS likely to trip a few things up, as it has been a basic hardware feature in most other cards since the Geforce 2MX.
One thing is certain, you WILL find things that will not run acceptably (or at all), despite this being theoretically DX9-capable hardware.
It wouldn't need a terribly expensive PCI-Express graphics card to wipe the floor with it, just so long as the accountants and marketdroid morons at HP actually left the thing with a usable slot to expand it - they've done motherboards with the AGP slot left out before now.