Trying to figure out how to get internet support without paying extra

We are in Fairfax, VA; called because cannot connect to the internet via desktop, WIRED connection.  No one will send someone out without charging a fee or making us pay some ridiculous amount for a "plan".  The lights are on, rebooted computer and modem/router.  Modem is so old there is no info on it so cannot try to connect it to my tablet or phone to see if the wifi is even working.  I think we need an upgraded modem at the least.  

Any leads on how to get through the phone tree to speak to someone who could actually help?