1998 ford explorer problems starting and shifting gears

This car has some kind of with starting. When I first noticed it, the car would not start after I tried starting smoke came out from the hood, and I noticed that the negative power connector grounding cable
had melted. Then it wouldn't start. I replaced the grounding cable and the battery connectors and the problem was no longer there. Then yesterday the same problem. This time the positice side connector had melted slightly and the car wouldn't start. It would just click and then all the power in the car was gone. To get the power back all i had to do was touch the + power side connection and it seems i would ground it and the power would comeback to the car and the lights were on. then try to turn over and it clicked and all power was gone. i reoved the positive side connctor, meshed the thicker wire (to alternator ?) and the ground (i think it goes to the ground, it connects to the left side of the body on a little circular device mounted on the car body) and once i wound the two wires together and reconnected the partially melted battery connector the car started. it always kinda has a slow turnover to begin with and then picks up speed in turning over and starts. I'm afraid this will happen again. what is the problem ?
also, the gears are very difficult to put into place. particular 1st and 2nd but someties they are easy and other times i have to push real hard to get the gears in. could it need lubrication ? what could be causing this and why does it occur some of the time and rather than always ?
thank you !
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It's a long shot but the extra load on the starter could be melting the cables.
Bill
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