This PC has really bad issues with Ubuntu and with Linux in general. The PC comes with an Intel HD Graphics 2000. (Sandy/Ivy bridge). When Ubuntu boots on this machine the screen flickers heavily, you can still manage to see a few things on screen but working on it wold be crazy.
Here is a video of the issue:
I tried everything, to try and fix the issue but to no avail: I tied 32 and 64 bits version of Ubuntu, tried various PPAs including glasen/intel-driver, xorg-edgers/ppa and the proposed repositories for Ubuntu 12.04 but nothing.
I tried with ubuntu 12.10 Alpha 3 and problem still persists.
The only way to get an stable image on the screen is to boot with nomodeset which only allows 1024x768 resolution and that is really low and also is not the correct aspect ratio for the monitor.
I tried with OpenSUSE 12.1 but with it all I get is a black screen (I tried with 1024x768 and VESA video modes). I'm pretty sure that this PC is just incompatible with Linux. Don't buy an HP All in One PC if you want to run Linux.