Car starts but the engine will not turn over

Not likely. More likely is that the starter, or the starter solenoid is bad.
This is the way it works. Turn key, car checks to see if all safety items are OK (in neutral or park, brake pedal depressed, etc), if OK then sends signal to starter solenoid to engage(it's basically just a magnetic switch), which allows the full power of the battery to turn the starter and engage the bendix, which engages the flywheel and turns the motor. If any of those things are bad, the car don't start. If it's the starter, the bendix will make a metallic click or thunk. If it's the bendix, the starter turns, but not he motor. If it's a fault in the electrical system, then no starter, and no bendix. If the battery is weak, the bendix may or may not click.
To repair;
1; starter can be rebuilt, including the bendix. moderately expensive if done by shop. Inexpensive if you can do it yourself. Warning - it's a PITA to get it out!
2; selenoid can be replaced. Usually inexpensive, except for shop charges. It sets on top of the starter.
3; If electrical; this can get expensive as it is labor intensive to track down the fault, even if the part is usually inexpensive.