This is very easy to do and I would never pay Linksys. Already mentioned, check drivers. If you must, download new ones for your wireless adapter (from a working PC if you can--or find your install disc that came with your adapter). There are specific ones off of Linksys to know your model number of the adapter.
Then, there are other things you can try. Are there any error messages popping up? Security concerns? Look in your Device Manager. Is your wireless adapter displayed in there showing no problems? Physicallky check your cables and wireless postition. You'll be surprised how many times I service these, that they're accidently bumped ever so slightly out of it's socket. A simple reposition, boom, instant Internet again.
After that, you can do deeper into the router configurations. To do that, we're going to need to know what type of router is used (the make of it, like Linksys, Netgear, etc). Maybe the ISP is too.
At this point, you don't need to give out PC specs as it is irrelevant. It's obvious to me that it should work on your PC since you've mentioned it worked on there before the restore.
