Crickets,
First, let me say that a wired network is more secure, more reliable, and more stable than a wireless network. Re-read Stumped Techy's first post for some of the issues you may be dealing with in a wireless network. Don't get me wrong, wireless is great, but IMO, it should be limited in application to: (1) computers that are mobile (ones that can easily be moved from one location to another); and (2) stationary computers that due to their location, cannot have network cable run to them. Personally, I have 3 desktop computers in my home, networked to a "wireless" router by network cable (the ends look like telephone cable plugs, but larger) and I have a laptop computer with a built-in wireless adapter that I roam around the house with while using. It was a bit of a hassle to run some of the network cable, but IMO, well worth it.
Second, do not confuse your cable modem with your telephone modem. They are two separate modems and do not connect to each other. The telephone modem connects to the telephone line and is used for dial up internet access (AOL), receiving and sending faxes, and any other telephony software. Generally speaking, a cable modem is used for broadband internet access. To set up broadband or wireless broadband, you only need to concern yourself with the cable modem, which I understand from your post, is in the garage.
Now, with that said, I'm not sure why the Cable Modem installer was so quick to put the Cable Modem in the garage and to tell you to go wireless. Did he/she not give you the option of installing another cable outlet closer to the Dell computer? Does your Dell have a wired network adapter? It sounds like you don't, but if you do, is it possible to install an additional cable outlet closer to the Dell desktop PC? I would recommend that, even if you have to pay for installation of that extra cable outlet. If you can, I would call roadrunner back out to install an additional outlet in proximity to the Dell and then follow the instructions which are obviously for wired setup. In addition to having a wired connection from the Dell to the router, it is also important (IMO) to have the cable modem and router close to your computer, because occasionally you will need to view the LED lights on the modem and router. I would not want to have to walk out to the garage everytime I needed to view those lights.
Another option is to go wired with the old Dinosaur Gateway. If it has a network port on the back, then you would need to run a network cable from the Gateway to one of the Lan ports on the router. Of course, you would need to be able to run a network cable from your basement to the garage. If the Gateway does not have a network port on the back, it will be easier and cheaper to find a network adapter to install in that machine (provided you have an open PCI slot) than it will be to find a desktop network adapter that works with USB 1.1. Then you would just need to run the network cable. There are websites that describe how to setup wired networks and even how to make network cables, if you are so inclined. If you decide to go that route, just post and I, or someone else on this board will post some links.
If you cannot go wired, then you would need to use your AOL account (through dial up access) to setup the router. You must have internet access to setup your router to go wireless.
Generally, in a network with a wireless router and cable modem, the setup is as follows: (1) the cable from the wall will attach directly to the back of the cable modem; (2) a network cable is attached to the back of the cable modem with the other end going to the WAN (internet) port of the router. There are no other cables involved. The main difference between a wired network and a wireless network (non-technically speaking) in your setup, is that a wired setup will have a network cable going from the network adapter in your computer to one of the LAN ports on the router, while a wireless setup will not.
I know there's a ton of information above and I hope it helps. OTOH, if you have any specific questions about any of the above, just post back.