No doubt it sounds like the starter stayed engaged, but if you shut it off within the first couple of minutes the starter may be ok. Im with Stuart, something isnt right on the battery terminal. In a very short amount of time the wires related to the starter and starting would get very, very hot. I would suggest back tracking all the related wires to make sure nothing melted down. Pull off the switch on top of the starter and make sure the contact didnt stick to the post.
If it turns out to be the starter, what will happen is that if the starter runs for a long period of time, the soldered pins that attach to the commutator bars will heat up and throw the solder out of the pins. This of course trashes the armature. You have to have a soldering pot to fix the armature.
Let us know what you find and if you need any starter parts or help private message me.
Ken