No Start - Hot cables - Dash Light On for no Reason

This is a Ford F-150 4WD pickup.
We are having a severe cold spell, well below zero temps. Yesterday I drove the truck about 7 miles without problems, except it
took forever to warm up, and had to be restarted about 10 times. (it does that all the time). Anyhow, that's not the problem.
After driving it all that time, I went into a fast food rest. and grabbed a few burgers. I was in there 15 or 20 min. When I got back outside the truck would not start. The starter clicked as if the battery was dead, and upon starting, the dome light went out entirely. It looked as if everything went dark, even the dash lights were out.
I let off the key, and everything remained dark for a few seconds. Suddenly the dome light came back on. I tried again, and the same thing. I tried a 3rd time, and this time I still only got a starter click, but the dome light did not go out entirely, just got real dim. I tried a few more times and still could not get any power to the starter.
I was beginning to think the battery was dead, even though it is a brand new battery about 2 months old. I popped the hood open and found the battery cables were hot (both of them). I jiggled the cable ends one the battery, and found the + one was a little loose. I tightened it, and got back in the truck. The same thing, only a click and dim dome lite. I went back and jiggled more on the cables, and noticed they were even hotter. I tried to tighten the nuts on the solenoid, but they were tight. I tried to start it, and the same thing. I went back out and banged on the solenoid with my hand. Got back in, and the truck started just fine. Unfortunately it killed (from the usual hard to start cold problem).
I tried to restart, and everything went black again, no dome light at all. I shut off the key, and one of the red dash lights was still lit, but very dimly. (normally they all go off when the key is off). That is when I noticed there was a small puff of smoke near the battery. I got a little nervous and grabbed my plyers and was going to disconnect the battery cable. Just then the dome light came back on. The cables were still hot, but nothing was burning. I banged on the solenoid again, this time using my plyers. I got in the truck and it started right away. I drove about 15 miles and came home. I shut it off and it restarted fine. A half hour later I tried again, and it again started fine.
WHAT THE F##K?
Is this a bad solenoid? I highly suspect thats the problem, except the part about the hot cables, and the smoke. And what the heck was the deal with that dash light staying on dimly when I shut the key off? I cant think what else it could be. I do know there is a switch underneath, which is connected to the shift lever, so it wont start in drive, but that thing used to cause problems when the shifter was out of adjustment, but it did not dim the dome lights and stuff, it just would not let me turn the starter.
There does not appear to be anything else that is not working, the heater fan, headlights, horn, radio, lighter, and other lights all work. The battery appears to be charging ok too.
Anyone have any ideas about this? I'm clueless.....
--
One other problem I want to mention with this truck. Why in the heck
do the doors on this truck refuse to latch tight when it's cold
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Replace that solenoid AND your starter, as well as cables.
snipped-for-privacy@UNLISTED.com wrote:

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