Battery or Electrical, won't start

The connections were already clean but I went out to clean them again when I noticed I finally got a spark when I connected my battery again. The lights came on many times but always died when I went to start it. Finally I left it on and wiggled the cord which kicked the fan on again but once again no start, Fifth time did it and it started. Do you have any further insight? Was this corrosion based or do I have a fault in the positive connection which leads to my engine? Meanwhile I am going to run it for a bit and shut it off to see if it starts without problem again, maybe even wiggle the cord again to see if the cord cuts the power again.

I have ruled out the drain, and there was no crossing of wires or reverse connection or anything. Both cables leading to the positive and negative are black; negative grounds to the body and the positive goes deeper into the vehicle. The battery I bought is brand new. What I had to do to get my car to start is prop the wire from the edge of the battery up with a sponge and turning my car to neutral in order to start it. It has had a 4 of 5 start ratio since and if it doesn't start I wiggle the positive again until my fan fire up and try to start it again. My connection to the battery peg is tight and clean, its only when I adjust the cable portion that I get a change. When I said spark I mean I could hear my battery actually connect when the two connection are tightened as opposed to earlier when there was no sign of power. Does this sound like my cable might have a break in it? Or does this have to do with my neutral safety which is giving me problems, 1 out of 3 times I have to start it in neutral. Thanks for all your feedback.