I bet all you have to do is re-flow the solder on the motor and speed control, or completely replace the wires and re-solder everything.
I know you don't feel comfortable soldering, but you really need to learn. First of all, pick up a set of extra hands at radio-shack or harbor freight. Then the next most important thing is getting a good soldering iron. A cheapo $15 radio shack one will not cut it. Get at least a nice 60 watt iron, your hobby shop probably sells some really good ones. Then practice on tinning wires using the extra hands. Then practice soldering wires together, etc... and start soldering everything you can, solder up some deans plugs.
But yea, I bet it is a simple fix if all you are doing is jiggling the motor wire and it works, just sounds to me like you have a bad solder joint or even bad wires. Bad wires can happen!
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