Coffee overflowing and spilling out of the...

Your coffee maker likely has the option where you can remove the carafe while it is brewing so that you can serve yourself in the middle of the brew. When you pull out the carafe in the middle of the brew, a small lever closes off the drip at the end of the basket (to keep the coffee from flowing onto the empty space where the carafe was on onto the burner).

Then when you replace the carafe, the lip of the carafe pushes against that lever and re-opens the valve so that the brew can now drip into the replaced carafe. Simple.

In your case, it appears that when you place the carafe onto the burner plate, it is not engaging that lever and opening up the valve; hence the valve stays closed and the brew fills over the basket and makes a mess, right?

So do this, pull out the carafe and look up where the pointed end of the basket drips into the carafe. You should see a lever, or plate that the carafe top lip hits when the carafe is placed into the burner plate. Once you find that lever, or plate, give it a push (like the carafe would) and see if it moves. if it does not, then that's your problem. It is stuck closed and won't allow the brew to exit the basket into the carafe. Clean it thoroughly if it is stuck and then see if works.