It definitely sounds like all you need is the driver for the built in network card. Checking the docs, the list of drivers for the Dimension 2350 is:
The latest version of these drivers are available on the support website. I'd try reloading the first four drivers in the order listed above to see if that fixes things for you.
If it doesn't fix things a relatively inexpensive solution is to buy a PCI network card (they range in price from $10 to $50 now, depending on what brand and speed you get). While a USB adapter can work, I've always preferred internal cards when possible as they are less likely to get bumped around especially on a desktop.
If the drivers don't fix it and your system is still in warranty (based on the model, I don't think it is, but it might be) you could call tech support to see about getting the hardware replaced.
Thanks for your advice. Please note that in my original post I mentioned that I tried installing the Intel 845 Chipset Utility, but was unsuccessful. The setup process progressed to 30% and then suddenly stopped, bringing me back to my original screen and giving me a little message in the taskbar that said "Device could be operating faster if I utilized USB 2.0 port." I've tried to install several times since then to no avail.
Didn't want to load other drivers in your list without having chipset loaded first because from reading other posts I see that is crucial. I've successfully opened the tower and replacing the ethernet PCI card seems pretty starightforward. Was going to upgrade my RAM anyway. Re: new card. Any suggestions? Brands that are better than others? Brands to steer clear of? I'm not all that concerned with speed, etc. - so long as I can get my internet connection working and this router set up again.
Try installing the USB 2.0 driver, then the chipset to see if that makes a difference since the computer complains about USB when you try to load the chipset now. At the worst, the USB driver fails to load the same as the chipset is doing.
My personal preference lately has been for Netgear 10/100 cards as the three I bought about 6 years ago are still running strong. However, there are probably better cards available recently for the same price, or possibly less (I haven't had to look in a while ).
With SP2 you shouldn't need the USB driver as it was included in XP with SP1 (the driver is for WinXP no-service-pack). I suggested the USB driver just to see if it would make a difference, as at worst it would not load because the system already has newer drivers.
Hmmm ... try going to Device Manager, and see if you can have it check for updates for the USB root hub entry. I don't know if it will work, but it can't hurt anything (it will most likely state "no newer updates found").
If you don't have the Desktop System Software (if the system uses it) and the Intel Chipset software installed then yes, that could easily be why it isn't seeing the network card. Those two 'drivers' are what allows Windows to properly see and talk to all of the hardware in and connected to the motherboard for the system.
If you have another network adapter you can load the drivers for it and connected it up to see if it works. You should not need to disable the integrated network adapter, although doing so won't cause any problems.