When I try to connect, the light on my adapter card flickers madly but the modem does not respond. Also the Network Center shows the green icon as though the wireless network was working.
Does this show that my adapter is working and I don't need to use ndiswrapper? Or what?
Off hand I'd say your wireless is trying to work, but you may need to reset the router or modem. Both my router and modem are Linksys, but separate units. Usually it's the modem that needs resetting, when this happens, but sometimes both. You could try pinging the router, then the modem, then something in the outside world.
If you can't reach the router, the problem is with the card's setup. If you can reach the router, but not the modem the router may need to be reset to see the modem. If you reach the modem, but not the outside world, reset the modem. I usually ping the DNS server next, and if that works, then ping Google. If I can reach Google, I can reach the world.