Get a wireless/WiFi Access Point. It's like a router but it's specially made for carrying your wireless signal around the corners, or up and down the floors. Put one by the entrance of the basement.
A common cause to your problem is that you purchased the wrong wireless adapter for that computer down there. You need to know your router's signal types/frequency before going out to get an adapter for a computer. Also, a so-so wireless product may very well have a poor antenna which greatly compromises the equipment's ability to receive the signal.