To answer we would first need to know what CPU was shipped with this system, there was a wide range possible. I also question your statement of a 320W PSU as it shows in the link that it was shipped with either a 240W or a 365W
https://support.hp.com/ca-en/document/c01570344
So far you seem to have a PCI-e x16 slot and full height cards will work.
https://www.cnet.com/products/hp-compaq-business-desktop-dc7900-core-2-duo-e8500-3-16-ghz-monitor-none-series/specs/