Windows 7 32-bit should work fine on this computer as long as you have plenty of RAM such as 3GB is best, 1GB bare minimum. GPU drivers are the biggest problem for a system of this age and it can be resolved by installing a low end modern video card that is better than the integrated and has support for Windows 7.
Specs I see for this system are: Pentium 4 2.53Ghz, came originally with 512MB RAM and 80GB HDD
This system wont run 7 fast, but it can run it if you have plenty of RAM ( memory ).
What driver are you trying to hunt down by the way?
I got Windows 7 32-bit to run on a 2002 model year eMachine that was running a 2.0 Ghz Pentium 4 and 1GB of DDR 266Mhz RAM. Biggest issue was that emachines only made XP and older drivers for this system, and Intel only made up to Windows XP drivers for the Intel 845GL chipset ( integrated video ). I was able to force Windows 7 32-bit to run Windows XP 32-bit drivers and get the 1024 x768 back vs the Windows 7 graphics of just 800x600 and 256 color setting.