To see if your router broadcasts its SSID you need to login to the router itself.
Open a browser and type your router's local IP adress in the adress bar (the IP adress will be in the router's manual, for me its 192.168.2.1 but it's diferent across the world and with different routers). You'll be presented a login screen. Type in your router's password, NOT the password you use to connect to the internet normally. After that, there should be a tab labeled Advanced Options, or Wireless Network or something similar, it's different with every router. Under those tabs you should be able to set the SSID and there should be an option to broadcast that SSID. Make sure that option is ticked.
When you've done that, normally the network will show up in the list of Networks when trying to connect from your PC.