Starter issues

Hey guys, haven't been on here in a while now. Well I've bought my dart back that I sold four years ago! Somehow managed to get a hold of the guy and ended up getting it back. It's a mess as it has sat for years in a barn and what looks like in a field maybe, as well.

Well since I've gotten it back I've freshened it up and added some parts, it's a 72 swinger 318/904 car. I have been trying to fire it up and hit has once... It started and ran for about 30 seconds and I turned it off.
Well, I went to start it up again and it cranked, fired up and was good til I heard the starter keep spinning. So I turned it off and the starter kept going.

My question is, is this a starter issue or a starter relay issue? With key off, I connect the battery cable and the starter will spin up until I pull the positive cable off. And it will keep doing the same thing every time I touch the post with the cable.

Does anyone know what the fix for this would be?? It just spins and spins and spins. Might I add that it Doesn't crank the motor. Motor doesn't turn, it's only the loud whining pitch of the starter spinning.

Any help would be appreciated.