Before I ask my question, I would like to make the point that I'm not entirely certain that my regular means of internet access are, in the simplest terms, "legal". Under normal circumstances, I would usually connect to a wireless network called "linksys" which I understand is a wireless router company. The only problem with that setup is that the router I own (or rather, my mother owns) is on the first floor of our house, and while I normally use my laptop on the third floor, I don't receive signal from our router. Instead, I believe I've been catching signal from a neighbor or something (Though I don't know how this would work either, seeing as our router is still closer, and I don't have an external antenna).

That's how it usually works for me. However, this week, I lost the signal for some reason, and not only the signal, but also, when I attempt to diagnose the connection problem, I'm told that the settings saved on my copmputer do not match the requirements of the network. And I know I never changed my settings, nor do I even know how. Since the network in question comes from an unknown source, I can't fiddle with the router. Is there any other way I could experiment with solving the problem? Thanks.

Sounds like the wireless owner has got smart to your piggy backing their unsecured connection and added some much needed security.
There isn't really any way around this other than configuring your own router for net access.

Is there any other way I could experiment with solving the problem?

If the owner of the wireless device that was providing your Internet access secured the device to prevent you from using it further, no settings experimentation will result in a connection. Alternative options to use Mom's router might be: A) get a better/external antenna, if available, for your laptop's wireless adapter; B) Move Mom's wireless router to second floor to improve chance of getting a signal; C) Replace Mom's router with an 802.11g or 802.11n model to improve range; D) run cable to third floor and move existing router to third floor.

I'd also suggest determining the configuration of Mom's router and its SSID (name of wireless network) to see if it is the one you've been connecting to all along. If you stand beside the router with your laptop, it should be the strongest network listed. Also, is it a Linksys router? Documentation for configuring the router is available on the manufacturer's website.

I'd also suggest determining the configuration of Mom's router and its SSID (name of wireless network) to see if it is the one you've been connecting to all along. If you stand beside the router with your laptop, it should be the strongest network listed. Also, is it a Linksys router? Documentation for configuring the router is available on the manufacturer's website.

Well, my mom's router is a Westell VersaLink Mo. 327W. And even when I tried putting my laptop right next to it, not only was I unable to connect to the network, but it wasn't even listed in the available networks at all. There's a buttload of networks that I'm supposedly "in range of", but none of them have any signal bars. But thank you for those suggestions, I'll try them out.

Your mom's router is a wireless one. Its generally provided by Verizon when you subscribe to their DSL service.

It could be that the router was setup to not publish its SSID. So you need to find a manual for it and see how to configure it.