Why is your car just barely starting when you just changed the alternator and the battery is good?

Can be loose or corroded battery cables. If you see a bulge in one of the cables, replace it. Can also be a defective starter. If the engine is turning over as it should but is just hard to start, you have a fuel problem. Replace the fuel filter first thing. You may also have weak spark plugs or plug wires. Depends on the age of the vehicle and mileage. ==ANOTHER ANSWER== It's difficult to determine what is wrong from just a description, but if you mean that the starter does not turn the engine as fast as you think it should there are only a few possibilities.

1. The battery could be in good shape but have an insufficient charge. If you're certain that the alternator is functioning properly, that's not the problem. Use a voltmeter and test the voltage with the engine running. You should be able to produce about 14.5 volts under normal conditions with the engine running at about 1000 rpm and just about everything on. (the big power consumers are the rear window defrost, blower and lights)

2. The starter motor could be severely worn and "dragging". When the bushings are worn out the starter motor will not turn easily and it can sound like a dead battery. You'll need to check the starter to see if it's pulling too much current. There are special meters for that, don't try to use your multimeter.

3. If the alternator is functioning properly and the starter isn't drawing too much current the only other option is that the starter isn't getting enough current. That can be caused by either a faulty battery or a bad connection.