Write a letter to Comcast, customer service, explain as you have done here, that you attempted to cancel service on [date], and the company's records should note this fact, that you have been given the run around since, and so you you are not liable for any charges after the date when you notified them that you were canceling.
This time period would not include the three weeks during which you agree to maintain service. But, from that point forward, you aren't responsible for Comcast's failure to terminate your services, because you terminated service legally, and from that point forward, you aren't liable for charges.
Let them sue you -- they'll lose, based on your explanation.
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