Sounds like the graphics card. Can you not test the graphics card in a friends system?
If not your best off getting a cheap £10 / £15 PCI-E graphics card to test the system rather than pay a shop to test. You can always sell the card on.
Check the forum classifieds or ebay:
New Dell OptiPlex GX620 ATI Radeon X600 128MB H9142 on eBay, also Graphics Video Cards, Graphics, Video TV Cards, Desktop PC Components, Computing (end time 23-Apr-08 23:09:06 BST)