It is strange that you seem to have network connectivity, without any network adapters showing in the Network Connections (ncpa.cpl) panel.
Have you turned off any startup programs, or edited the registry lately?
What does the Network and Sharing Center show for a type of network. If it is a wireless one, there should be an option to manage wireless networks in the upper left of the window.
All I can suggest you do, is uninstall the wireless adapter from Device Management. When you do, also remove all drivers for it. Hopefully Windows will find it again, or you can load your driver.
Edit: There is a service responsible for the wireless configuration. You might check to see if it is running. Open the Services.msc panel and see...