Dell Dimensions 2100 and wireless networking

This pc does have ethernet.It was once hooked to the cable modem via ethernet cord.

Regrettably, that machine has no on-board Ethernet adapter.  In order to attach to your router you will need to purchase a network interface adapter card that installs into one of your internal PCI slots.  You can purchase either a standard Ethernet adapter card, or given that you have a wireless router, you can purchase a wireless network adapter.  Either should come with a utility CD having appropriate drivers that will likely need to be installed before you insert the card into the computer.

If an Ethernet card has already been installed you should simply be able to connect a cable from the computer to one of the ports on the router.  I must assume something has been left out of your description as I don't understand why there should be a problem in that case.

Are you certain that the computer was connected via an Ethernet cable?  Some cable modems also allow the use of a USB cable which is not the same thing.

I do not want to connect via ethernet. I am trying to connect it to the wireless router that is connected to my main pc.

Ok I see what you mean.

Now I have another question.Would I be able to install the router onto the kids pc and run mine from theirs(I have an hp pavilion a705w running windows xp home) or do I need one of those 2 wireless adapters still?

First, I realize it's only semantics, but you need to know that the computers attach directly to the router.  It is possible to run a connection through another computer first, but that is usually more difficult to arrange and totally unnecessary most of the time.  The router you have has space for four Ethernet connections and probably up to fifty or so wireless connections.  You can look at the wireless port as though it were an extension of the four physical Ethernet ports.

If you wish, and it is more convenient, you may put the router near the kids pc and run an Ethernet connection directly to it.  You may then use the wireless port to attach other pc's, including any laptops you may have.  Desktop pc's do not normally come equipped with a wireless card.  Most of them do have built in Ethernet ports.  I don't remember ever seeing a catalog that offered a wireless card as a possible configuration of a desktop, but it's not impossible.  Laptops often do have the option to order a built-in wireless card with your laptop.

Your Pavilion almost certainly did not come with a wireless card.  Therefore if you wish to associate it with your router you will need to purchase one of the two adapters I mentioned earlier, unless you wish to connect via Ethernet.