1990 Mazda Protege Mystery To ME

Well my car is having issues I recently purchased this vechile off of a friend and all he sadi that needed to be done was to put a new altenator in. Did that, the car still didnt show a charge. So we tested the old one and it tested good. So we then installed the old one. We run a new lead wire to the battery from the altenator and it showed 14 volts. Now the problem is the the car will run fine for a small ammount of time, we will say 10 minutes, after that it will misfire then jerk hard, and after that it will then die. And it will not start back up for a long period of time. After the car sitts for a while it starts back up but then it happens all over again. After that happens we tested the coil and there was no spark coming out of the wires or even the coil itself. I get no check engine light, on light going off is the belt light. I have no idea what is wrong with this car and I would really appreicate it if you guys could help me, I need the vechile to travel back and forth to work.