How can I make my computer stay connected to the internet -reloaded windows

Next time your online (like now) make sure theres no programs running that need internet and then look at your modem and make sure the lights for traffic (upload/download) arnt flashing frantically. If there not then that can basically rule out anything dodgy on your computer (some dodgy things wont get activated until computer has been rebooted).

If your sure you clean of adware/spyware (use program like Lavasoft Ad-aware and Spybot S+D) and viruses (hopefully you will have your own anti-virus installed) then if you definately have your network drivers installed i would contact your internet service provider (ISP) - it could be a problem their end.

It sound like your friend used your recovery discs. I wouldn't be suprised if there were other devices that might need tweaking as well. I myself have a scanner,video card and monitor that all have "special" drivers. But for your modem i would go to device manager and remove it, then use the install disc your service provider gave you when you picked up the broadband service.