You need to check the IP addresses of both machines when they are connected via the wireless.
Some questions to answer:
- Are both machines getting IP addresses?
- Are both machines getting the same IP address?
- Is the same machine always able to connect and the other one not?
If 1 is false or 2 is true, then you have a networking issue. If 3 is true, then there may be an issue with that specific machine.
There are 1000 reasons why a machine can't connect to a wifi connection. The hardware could be too old to support a specific security protocol, hardware could fail, etc.
Leave a comment if you notice anything strange with investigating these questions and we can go from there.