This is your computer?
You installed the 32bit or 64bit version? HP Compaq dc7800 Convertible Minitower PC
And you've gone to this page? HP Compaq dc7800 Convertible Minitower PC*-* Download drivers and software - HP Business Support Center
Win 7 Ultimate wasn't listed so I followed the links from Win 7 Professional (32-bit).
The index page is here. HP Compaq dc7800 Convertible Minitower PC*-* Download drivers and software - HP Business Support Center
It looks like the first two upgrades for Windows 7 are BIOS and Chipset drivers
and that sounds to me like a good place to start as both of these will help Windows 7 correctly identify the hardware on your computer.
I would first install the chipset drivers which are basically inf files that correctly describe the hardware configuration. A BIOS upgrade is a little more tricky if you've never done one before, I would visit the Hardware & Devices sction of this forum and post a question (re: BIOS Upgrade) there.
Don't know if there's an easy fix as it looks like a couple of things need to be updated first.
Go for the chipset drivers and see if Win 7 recognizes your hardware.
Also, one other question... did you install Windows 7 over the top of your previous operating system or did you wipe (format) the drive and do a fresh install.
The first two