Help! no idea whats wrong

[SidewaySupra]

Hey guys, I bought a clean 89 supra a month ago its na and its got 71000 miles on it. Heres the problem:
A couple times my car hasnt started right away I thought the clutch wasnt in all the way cuz id turn it a couple times and it would start. When it doesnt start it doesnt even turn over. Last night I drove to work about 30 minutes in 85-90 degree weather and the car drove fine. A few hours later i unlocked it and opened the door the alarm went off and it wouldnt start. I assumed it was because of the alarm but i reset the alarm and everything and nothing worked. after 20 minutes I gave up trying to start it regularly and flintstoned it. (had people push the car and pop the clutch) that worked and it drove fine. As I was driving though there was a high pitched whining noise that got louder as the revs got higher. There was a funny smell its hard to describe but no smoke. Could this all be a problem with the alternator? I read somewhere that the problem starting is an old trigger wire that isnt as conductive as it used to be because its old and hot. but that doesnt explain the sound and smell.
Has anyone else had this problem? I need help please