Are you sure the button is stuck? This happened on my car also but it was actually just the plastic sleeve that covers the brake handle. It slips up the handle and covers the button so it appears depressed and doesn't allow you to push it in. Make sure you shove the cover all the way down and back before you do anything else. I think it should be secured there with some sort of snap but I think mine may have cracked. Good luck!
After a nice talk and adjustment, it is working properly. Yes, it makes sense that the cable is working if you feel resistance but you really don't think about it when it's not working.
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