Ignition stuck in the on position?

One day my car wouldn't turn off. I removed the ignition fuse to shut the engine off. I put it back in and it started right up. The key also comes out while it is in the on position, I'm guessing because it is so worn out. I also removed the cluster fuse so they would go off. I left it alone for a day, and the next day the battery was dead. I ordered a remote battery shut off thinking I would be lazy and just drive it like that. . I figured I should charge the battery before I installed the shut off switch so I used my jump box to start it, it runs for a minute but before I can get out and unhook the box it shuts off again. Can anyone please give me some advice??