Thanks Mango...From your router's control panel, navigate to Advanced >> Setup >> WAN Setup. Look for the option "Disable SIP ALG" and place a check in that box. SIP ALGs very often don't work properly. If it is currently enabled, it is more than likely causing your problem.
Under Advanced >> Security >> Block Services, be sure nothing is there that could be causing your problem. Also, check your port forwarding and remove or disable any port forwarding to your ATA.
If neither of those solve the problem, navigate to Advanced >> Administration >> Logs. Clear your log, make a test call to cause the problem, and then refresh the log. See if anything there gives you a clue about what is going on.
If none of those work, consider installing Tomato firmware on your router. Tomato is a third-party firmware which happens to be VoIP-friendly. If you do this, navigate to Advanced >> Conntrack/Netfilter, disable SIP Helper (if that option exists), and set UDP Timeout Unreplied to 10.
Good luck. Let us know how things go.
I ended up with no dial tone.If possible, don't use DMZ as it's a security risk. However if things absolutely won't work any other way, then be sure your ATA has strong passwords.
If the fast beeps/dial tone happened after my suggestions, try reversing them one at a time to see which one caused the problem.
Keep us updated on how things go.