My first response was going to be, "that will not work because you cannot get enough current through the tiny jaws of jumper cables", but you proved me wrong. So with a positive and a negative temporary cable in place, the starter cranks the engine just fine, right? Now just remove one of them and see what happens. If you have just the positive one still in place and it doesn't crank, it is the negative one that has the problem.
Oops; wait a minute. You said you put the negative jumper cable to the frame, meaning the body? If that solved the problem, without that jumper cable you should not have dash light, head lights, or anything electrical working, including the starter solenoid. If that is correct, look at that negative battery cable clamp. It will either have a second, smaller wire in it, or the fat one going to the engine block will have a crimped-on strap in the middle. Whichever you have, that gets bolted to the body. The entire drive train is mounted on rubber mounts to reduce vibration, so for the return circuits for all the other electrical stuff, there has to be a ground wire bolted to the body. Check if yours got left off or is corroded off.
If you meant to say the negative jumper cable is attached to the engine, and that is when the starter works, that cable has a bad connection or is corroded away under the insulation. To verify that, use a digital voltmeter set to the 2.0-volt scale. Put one probe on the battery's negative post, and the other probe on a paint-free point on the engine. Electrically-speaking, those two points are the same points in that circuit, so the meter should always read 0.00 volts. However, there is always a little resistance in any wire or cable, and current flowing through that resistance will cause a slight voltage drop that can be measured. (To be technical, that resistance is way too small to be measured with your meter, but we can measure the results of that resistance with this voltage drop test). During cranking, which is when the really high current flows through that cable, the most voltage drop you're allowed to have is 0.4 volts. There is more to the story, but we will discuss that when the time comes.
If that negative cable has a bad connection, your meter will likely display an over-range condition, meaning more than 2.0 volts is being dropped. That problem will not cause the head lights to dim during cranking, and the battery cables will not get hot, because too little, or no current is flowing.
Instead of a digital voltmeter, you can do that test with a test light too. If you see any glow in the bulb's filament when trying to crank the engine, there is way too much voltage drop. The problem is that will only show a major defect. 0.5 volts is too much drop, but a test light will not come close to showing that.
Sunday, July 2nd, 2017 AT 10:54 PM