Approximately what percentage of incoming calls on the Charter line are affected? If it’s, say, 20% or more, you should be able to cause the problem at will by calliing in from your mobile, repeatedly if needed. This should make troubleshooting easier.
What appears in the Asterisk log on a failed call? Does it look like the call was abandoned by the caller, or did Asterisk answer (or attempt to answer) for some reason?
jmelson The callers hear ringing, then it changes to a busy signal.
Always after the first ring, when you answer, at random?
Have you tried rebooting the Charter modem (may take work if it has a battery backup) and also the Asterisk system?
Assuming that you can easily replicate the problem, you could try temporarily disconnecting the Charter line from the telephony card and connecting it to an analog phone (preferably line powered and corded). If that also fails, just open a ticket with Charter. If it works fine with the analog phone, try swapping the line ports on the telephony card and see whether the trouble moves to the AT&T line.