I'm having problems starting my cavalier the starter just barely turns the motor over and then it starts right when you think it's going to quit it's got a new battery with 12.5 volts and yet it still does this the car has 125,000 mi.

 

There are a few possible reasons,
Corroded battery cables,,,,poor connections at the starter or engine,,,, tired starter.
That is not a lot of miles for a starter, but who knows how many times the vehicle was started , if the starter is original , and on there since 2005.

 

After confirming that there's no corrosion at either end of both battery cables, and confirming that their connections are tight, buy a new starter. Not a cheap rebuilt/remanufactured starter but a new one. (To check/clean the battery cable connections at the starter and engine (ground) remove them and use sandpaper or a file to clean the connections to bare metal.)
However, if you have access to a battery charger, or if you can hook jumper cables to your battery from another car's battery, or if you can borrow a battery from another car, and your car then starts normally, your 'new battery' is no good.

 

Disconnect the ground cable (black, negative) from the battery before doing any work on starter or cables.