Thank you for the help ECU-MAN! I think that may have been the problem. Got my dad to help me out on resoldering it and so far these past couple of days, I haven't encountered any problems yet (touch wood). Really hope this was the problem.
Yes, when it stalls it still has power and the car still cranks. The engine just doesn't turn on. After a couple or so minutes of waiting, I'll try starting it up again and it'll come back on as if nothing has happened.

