You didn't mention the make and model, that might help.

That the lights and radio were dead is telling. Some cars haqve the battery + going straight to the starter motor and the solenoid is mounted right there and also serves to engage the gear to the flywheel. It sound like that is where your bad connection is. Older GM cars were like that. Over the years the vibration can make that nut loosen up. Now that you got it to connect by jarring it (the door) and welded it together (by actually starting it, the connection might stay good for some time. However it is still unreliable and unreliable **** in cars is no good.

since you say you don't see any fusebox looking type of thing nearby, the connection point may well be right at the starter. I would crawl down there and undo it and redo it. Maybe brush up the connections a bit. I would say to test it by trying to turn them but they might be welded together so that test could easily yield a false negative. (no pun intended this time) If you redo those connections, remember to disconnect the negative battery cable first. When spark fly from something like that they can hurt your eyes, burn your clothes, and if there's ant gasoline laying around you might find out just how good your insurance is.