Wireless only works when second laptop is connected

My roommate and I are struggling with a bizarre connection issue. We have two Windows laptops trying to connect to the same wifi network. The wireless on the first only works when the second is connected. That is, if the second is connected, everything is fine, but as soon as the second disconnects, the first does as well. If the second is disconnected, the first simply cannot use the network. It is possible to reconnect for a few seconds, but it always drops. We're not aware of any other connection between the laptops. Also, a few weeks ago this issue did not exist.

We're happy to provide any other information that might be helpful. Thanks in advance for any advice! :)