Hi, and welcome to Geeks to Go!
What you need to determine is if the problem is due to the wireless card, the Linksys modem, or Windows/Internet Explorer.
If possible, try to connect the computer to the modem directly using USB (if supported) or ethernet cable. You can pick up a cable at Wal-Mart, Best Buys, Comp-USA, Radio Shack, etc. If no lock ups, then replace the wireless card.
Did the person who built your computer provide the wireless card and modem? If so, he/she may be willing to test them for you. If the computer they test on has no problems, then it's something with your computer.
You might also want to test the RAM. (the following I snagged from Keith - thanks!)Click this for a guide to using memtestClick here to download memtest
Allow this to run overnight, if possible. Report any errors.