Car sputters to life then runs fine?

I have an 2002 Ford Focus and for the past couple of months I have been having an issue with starting my car up. About a week ago my car died on me completely and would not start so I figured that the problem was my starter because of the weak start I've been experiencing for months and the fact that my lights and everything were still on. I managed to get it towed to a mechanic thinking that it was the starter just to find out that the starter was fine and that the car went back to running perfect after a full charge, apparently the battery was almost completely dead. I went to autozone to get the battery checked out and figured out that everything was okay with that. I got the alternator changed and figured out everything was fine with that also. I unhooked my sound system from the battery and am still having problems. At this point I have no idea what it is because I've had problems with this in the past and resolved it with a new alternator. At that point in time all the fuses were checked too and found out that nothin out of that was draining it. I'm completely lost and now having to have it took up to someone who will have to look at it for 70 dollars and still am not guaranteed to find the problem after that. What other options do I have left to check?

#1 batteries need to be test for amps, alot of high school student work at parts houses and don't know this, you can have 12 volts and no amps, amps start the car volts run everything else, thats what the cca is on your battery,
#2 if a battery is ran dead it is very rare it will ever take a full charge and hold it, usually it will say full then it will blead off, it all depends on how many times its been ran dead and the age of the battery, and brand,
#3 was the alt tested multiple times, they will test good then right after on the next test they will test bad, it all depends on the RPMs the tester is running at, alts should be around 14 volts constant, a bad alt will sometimes test 14 at 2000 rpm but only 8 at 1200, thats why you do multiple test, also heat, dirt, grease /oil will mess with the test so make sure you clean the alt as best you can before the test,
#4 if your car has a dead battery after driving, you most likely have a bad battery, it was running on the alt and that will burn it up if it goes to long, if the car dies and won't restart you probly have a bad alt, easy test wait till its dark and start the car, turn on you head lights high beams, now start turning things on like the heater fan to high if your lights go dim you got watch your volt guage it should drop just a little then almost immediately pick up to 12 to 14 volts, if it doesn't rev engine and see if the lights get brite then dim when you let off, thats usually a bad alt

If its driveable, take it to Autozone and get them to scan the computer for diagnostic trouble codes. You can have codes stored even if the check engine light isn't on. If codes are present, this will either tell you exactly what's wrong and causing the problem or it will give you a good place to start trouble shooting. If the battery, alternater, starter, and fuses are all ok double check every cable/wire attached to the battery, starter, alternater, and engine/body/frame grounds. Make sure they're tight and corrosion free. The grounds on a computer controlled car are very critical to proper function because computer circuits and sensors work on very small voltages(5volt reference signal)There are a few sensors that cause hesitation(TPS, MAF)The maf can be cleaned withs electrical contact cleaner.Sensors that cause hard/no start(MAP, Crank, Cam)Check the vacuum hose to map sensor for leaks and deterioration. The ignition module is another likely culprit.Autozone can test this module if you bring it.