If the router works fine for Cat5 Cable connections ( coax ) and wireless is not working, it is possible that the routers wireless is dead. However I would first start with looking to see if this router is still transmitting a signal. When searching for wireless connections you should see it listed unless you have it set to hidden mode. If you dont see it and you didnt intentionally hide it, then you can try a hard reset of the router. But before doing this, go in and write down any special configuration data such as port forwarding info if you use Vonage for example etc as for the hard reset will clear this and kill your phone if you have vonage or another VoIP phone. Also if this requires authentication to say a DSL connection vs Cable Broadband be sure to have that info available written down too.
Hard Rest is easy... just find the small micro button that usually says reset next to it and power the router off first. Then hold this reset button in and power on the device while this button is held in. After the router boots up usually 15-20 sec or so you can release the push button and it might go through another warm boot before coming up to work with it.
If you have DSL to this router you will need to connect to the router at its default IP address via Cat5 Cable and use the default password to get into it. Then you will need to set the authentication info.
If it is Cable Broadband you just need to access the router via default admin user name and password that is either on the label on the router or in a installation manual that came with it or search google for it from another internet access location for that routers specific model.
One in you can set up the wifi which should be wide open ready to allow devices to connect with no security which is usually default for most wireless routers. At this time you should also be able to see the router from a wireless device as available and insecure wide open for a connection. If you see it now and didnt see it before then simply with the system connected directly to router via Cat5 cable set up WPA2 or other security option for wifi and then connect the wireless devices to the router, lastly after adding back any port forwarding etc, change the password on the router from its default to something only you would guess. I usually use a permanent marker and write the password on the plastic bottom of router, so next time I have to get into it, I am not guessing password and just look under it and get in, otherwise its a hard reset and lots of configuration since I have many port forwarding and other custom settings as well as mac filtering etc.
If after the hard reset the router is not showing wifi and going in and confirming that wifi is enabled its still missing then the wireless is bad on this router and you will need to buy a new one. Before doing this make sure the antenna's are not damaged and screwed in all the way if the type of router that allows for antenna replacements.