You need to know what your bank's dispute procedures are, to begin with. I would be very surprised if a bank were to just flat out refuse to open a charge dispute for no reason. Is it possible you didn't go about it the right way? I'm not saying you did anything wrong, but each bank/card issuer has a set of procedures for how charge disputes are handled, and if you didn't follow them properly, they are unlikely to help you. That being said, if my bank was that unhelpful, I'd be looking for a new one!
The other aspect to consider is talking to Comcast about the issue to see if maybe they'll do a bill credit if they aren't willing to refund your card. That's always an option. Comcast should be able to investigate the incident and (if the call was recorded, which it usually is) make it right with you.
In any event, make sure you document everything you do (when you called, who you talked to, what the conversation was) so that if you have to go further with this then you have proof you made good faith efforts to resolve it.
My experience with Comcast (and I'm only speaking for myself here!) has been that they're generally pretty good at resolving issues, including sending a tech to my house on July 4th within an hour of my call at no charge for an issue with my Internet.
Start with talking to Comcast. Keep your cool, and if you feel you aren't getting anywhere with the agent you speak to, don't hesitate to ask for a supervisor. The same is true with your bank. Ask to escalate the issue to someone higher up the food chain, because they have the power to do something for you. But I can't emphasize enough that you have to keep your calm. If you go off the deep end then whoever you're talking to is much less likely to want to help you or go out of their way to do something. Remember, they aren't the one who made the mistake, but they are the one who can do something about it.
I hope this helps.