Having looked at the card and connectors again, I'd say they look identical to phone connectors. I wasn't sure at first because I had a look at some pics of ethernet cards and they looked similar to what I have. I'm still a little confused though because if device manager says the modem and its drivers are working, why is the same modem showing up as an unknown device in a different section? Also, should I uninstall the software before the card is removed or does that not make a difference?
Sometimes they show up as multiple devices to support modem features. For example, some modems will show up as a sound device; Many video cards appear as a sound card as well because of their HDMI capabilities. Some later modems included driver software that was designed to allow the modem to be used directly as a network device directly. For Dial-Up, for example, typically what happens is you would run a separate program to connect; that program would establish a connection and keep it alive. After that, the software would activate a second driver so the system could see a "network card". The network card doesn't actually exist and is entirely software that mimics a network card to provide network connectivity through the modem, but in this way network-using applications don't need to care how the machine is connected to the internet. Usually that driver is only enabled or made active when you run the appropriate application to "enable" it, at least as far as I recall. Otherwise, it is either invisible, disabled, or appears "broken".
As for software/driver removal, I usually never bother to remove the software for a device before removing it, though it doesn't matter either way. The way windows works when it starts up is it basically looks at all the devices and looks for installed drivers for them. If one removes a device, windows won't really care since it simply no longer looks for the driver to initialize. It's usually a good practice to remove them however unless you plan to use the device again.
Ideally I'd like to get a couple of upgrades for this old pc, so it's compatible with wireless routers. The tech guy at my ISP told me the pc needed an ethernet card and something about being wireless or wifi enabled but he was somewhat of a tech snob and wasn't very specific. Apart from the card do you know what else I'd need for a wireless router? Would I need to go hunting around for old cards since because of the old motherboard?
A wired ethernet card would not be directly helpful for wireless connectivity. What you would need instead is a wireless card, in the form of a wifi(802.11g/n) card. You can also find wireless adapters in the form of USB sticks, but given your other problems with USB it might be best to avoid those (and they are more expensive anyway).
I was thinking of having the usb connectors changed to 2.0 ones. Can that little usb "cube" be removed from the motherboard and upgraded or would I need a new mobo? I was under the assumption that old hardware only works with other old hardware (especially 10 year old motherboards).
You cannot replace the on-board USB connectivity with a newer one, but you can add a new Root hub in the form of an adapter card such as
this one. I have two cards like this that I've used in a few older machines, the first one I installed one into was a machine that was originally sold in 1998-1999, and it worked fine. This one is particularly odd since it has a connector that is inside the case, too.
The little connector box that sticks out of the motherboard is really only the connectors. The actual logic that deals with the USB connectivity is part of the motherboard chipset, and so cannot be removed or replaced. One can instead just add a completely new USB Root Hub; one of these cards adds a second USB Root hub that is an "Enhanced" controller, which is the term used to describe USB 2.0 root hubs. I've not had to use it with anything earlier than XP, which was able to automatically detect and install them without any additional software.
