Specs on TonyR's computer, UKT Support - Advent QC8003 PC
And yes the 9600 GT is far better than the integrated Intel video. If you want to connect via HDMI, if you can take a good look at the 9600 GT and find out who it was made by. And no it wasn't Nvidia, it will be one of their AIB partners (EVGA, BFG, XFX, Zotca, etc). Once you find who made the card then try contacting them and asking for a DVI-HDMI adapter like this (it is not a standard DVI-HDMI adpater, as the one that comes with most cards is pinned differently so that it can carry audio),
Most that I have seen that have contacted the manufacturer have received the adapter for a low cost, and in most cases free. Unfortunately the 9600 cards were hit and miss as to whether that adapter was included with the card. If you didn't get one maybe even contact the place you bought the PC from and see if they have them.
While you're at it if you want audio over HDMI with the 9600 GT you will need one of these cables,
which connects the SPDIF header on the sound card or onboard audio to the corresponding SPDIF header on the video card.