Greetings..
On the older models there is usually a mechanism to physically open the door. I state that since some of the top of the line more expensive (and thus exclusive) models had a servo to even open the cassette door - however, that wasn't all that common.
Simply put, without pulling out the trusty Xcelite phillips-1 head screw driver and removing the top to actually reveal what's going on - it's merely a guessing event. Sooner or later, you, or someone else, is going to have to actually take a look to see what the issue is inside the deck.
I will state that if you're not used to doing this type of work and don't have the tools or experience to do this, save yourself a great deal of heartache and take it to someone that HAS done this type of work before. If it's an acquaintance, there's nothing stating that you can't watch them as they reveal the problem and determine the necessary steps to "fix" the anomaly.
You are correct about one thing here though, it's never a good idea to force anything regarding an audio cassette deck.
Cheers, Mr. Mentor