Car won't start

Hello Everyone, So I have a question about my Mitsubishi. We have had the
car for around a year and a half but we have not had it on the road. So It's
been sitting for around a year. I wanted to get it running so I started trying
different things, at first we thought it was the battery So we bought a new
battery (I don't remember if it started the car when we did buy a new one)
Anyways, So we tried jumping the car and it doesn't work no idea why even
got someone to double check to make sure if I was doing it correct.  We took
the battery out of another car and it started up and the battery that wouldn't
start my car we put in a v6 mustang and it starts just fine. So I thought the
problem was fixed but the car isn't street legal yet so I just started it up every
few days and let it run for 10-30 minutes but everytime I started it took
several turn overs for the car to start and then after running for a while
whenever you turned the car off you had to wait like 15 minutes before I
would even start again (wouldn't turn over) So a few days ago I went to try to
start the car and it turns over one time then nothing. So went to autozone to
get battery charged and same thing, Turns over one time and no more. I just
don't know where to start we replaced the battery terminal clamps (Don't
know actual name of it) I asked someone I know that works on cars what the
problem it could be that It doesn't start after running for a while and he said
something about sensors, Asked auto zone they said something about the
Starter or something getting to hot because it sits under the manifold but
There is already a heat shield there. Where Do I start? I'm trying to avoid
replacing the starter Cause they cost $150 at auto zone and the battery
cables are connected to the fuse box or something so don't know how to
replace those please help sorry for the messy details