If you can see Earthlink listed in the Network Connections, then click on it.  Now check in the Properties button to make sure the right modem is selected.  Also check if your user id, password, and dial number are correct.  If you think the modem hardware is bad, run the Modem Helper to confirm it and follow the instruction there and you might be able to solve the problem. 

If you don't see Earthlink listed in the Network Connections then it was not properly set up.  If Earthlink provides a Disc with setup package, run it.  If you do it right, it should place Earthlink in the Network Connections area.  The Modem will never be listed there.  You can check Modem by going to the Control Panel>Phone and Modem Options>Modems.  If you see a modem listed here, then it is your modem.  You can run Diagnostics there by clicking on Query Modem or run Modem Helper on the Desktop to make sure the Modem Hardware and Software work properly.  Make sure the modem is not disable in the Control Panel.  If the Modem Helper cannot detect anything wrong with the modem and Earthlink cannot be listed in the Network Connections then problem is on the Earthlink Setup Disc or human error during setting it up.