Are all or any of the other family member's computers exactly the same as yours including their wireless adapter, wireless adapter driver, version and date?
We're trying to help. Is this a laptop? If so have you attempted to use the wireless connections anywhere else, like a local library, coffee shop, McDonalds, or other hotspots or a neighbors or relatives house?
If you have and it works then the problem is between your specific adapter and your router, they are not communicating and you need to address the cause. Do you know the router is broadcasting the SSID, do you know the SSID and the length of it.
There are a multitude of other options that you can try but you need to confirm that your driver version and date are the most current available, sometimes those atheros cards can be finicky.
You can try changing the channel on the router try 3 or 11, you can change the encryption on the router, try running it open, if successful try WEP, if successful try WPA and or WPA2,.
We understand that you "just don't know what the problem is" and neither do we, so we are providing some suggestions for you to try. The fact that other family member laptops connect fine is a good thing but does nothing to address your issue. Your laptop is likely unique and may have hardware and software products installed that are not present on everyone elses computers. We have to start somewhere and the fact that the ethernet adapter works fine is a good sign, but the fact that the wireless adapter shows "Not connected" as its' current media state property is not. So it's driver update time or driver rollback time if you allowed the Windows Update Utility to Install a recent device driver update for your Atheros wireless card. Or you need to address the encryption currently running on the router or the channel to see if your laptop if it is a laptop, will connect with different settings.
Regards
Randy