Yes it does, find out what network card your model has, get the name and chipset number. I find it strange that dell would not have it.
If it's a popular brand like Intel, Realtek, Atheros, you might get by finding 32bit drivers on their sites. I would never run Win7 in 32bit mode, XP is a lot more efficient. If the machine is 64bit, why not get Win7 64bit ? It will perform faster.