Verified dial tone by putting a standard telephone on the end of the line cord ?
If you have dial tone check the pins where the line cord plugs into the modem (normally does not happen but they can be mis-aligned or due to humidity corrode and eventually break off).
If no dial tone check the jack for the above problems.
Line cord is plugged into line not phone jack on the modem ?
Was this modem ever working ? New modem ?
Make sure you only have one modem loading.
located in Control panel -> modems should only be the one you are using.
When you attempt to dial there should be a soft click from the modem/speakers (relay/electronics transferring from on-hook to off-hook). by changing the modem to not check for dialtone and inserting several ,,,, at the beginning of the telephone number, to give it time to activate, you could force it to dial out. located in modem -> properties -> specific modem properties -> connection just uncheck wait for dialtone. If this is behind a PBX or small Telco the tone generated indicating dialtone may be out of tolerance for the modem's tone sensors.