Serious wireless internet problems

Okay. So I recently got a laptop computer, my first, a Dell Inspiroin 1300, running Windows XP home edition. We bought a wireless router, a Gigafast. Two desktops are hooked up to it by wire, and they are fine. We went through all the steps to set it up, invented a network name, and so one. When I got it, I couldn't hook up to it, but I could to some randomn network, My WLan. SO that was fine. Then, about two days after I got it, I was working on the internet, and the internet just disconnected itself. I tried to reconnect it. When I did the connect to the network thing, the bar on the network screen with the name of the network got a little message on it saying not connected, but the little pop up screen that shows you it's connecting says connected. And I can connect to the internet again, but again, it just randomnly disconnects, stills say not connected on the screen, but when I click on the bar, it asks me if I want to disconnect. THen I take it to school, find two wirelss networks there, both say I;ve connected to them, with good internet signal strengh but the internet doesn't work on either. Then, I get back home and the network that previously called itself My WLAn, now bears the name of one of these school networks, then changes back into My WLan, and back again. This is driving me crazy. Plus, all these other randomn networks on here at home,a dn I can't connect to any of them, including my own. What is going on, and do I fix it?