Unless you have the modem speaker-volume turned down or off you should be able to hear the modem 'pick up' the phone line and dial. Even if the speaker volume is turned off, you should be able to head the modem dialing out if you lift the handset and listen to the line.
If your modem is not transmitting signals to the phone line:
If you have an IBM type computer, do you have a conflict with another hardware device? The most common conflicts are usually a mouse, cd-rom (or second hard-drive controller), or network card.
All modems can be configured by sending commands from software. Most communications software sends an initialization string to the modem when you start the software (or dialing process). If this initialization string is wrong your modem may not respond normally. External modems usually have lights/LED's that blink when commands are received... if the lights on an external modem are not lit check the power switch/cable... if the lights do not flicker when you try to dial the modem is probably not receiving data from your software.
If you are having trouble connecting to VTN you should try connecting to another computer system. Local computer bulletin boards (BBS's), libraries, or friends with a computer configured to 'auto-answer' offer an opportunity to test your ability to connect to another system.
Software problems generally fall into two types: