Lights come on but the car will not turn over and I have a new starter

Try new starter or even try bridging a screwdriver to engage the starter manually that will tell u if its starter or something else

Check fuel pump fuse.

with lights on and when you engage starter, do lights dim?

If the cat is not turning over with a new battery and new starter, make sure the starter is getting correct power. Impalas are tricky since it is front wheel drive. Be sure the cables connecting the starter are fully tightened or plugged in, and be sure it is grounded properly. If your interior gets power there is some issue going to the starter or coming from it to the engine. When you turn the key to start, does it have any sound coming from it?

Have you checked the starter motor and solenoid? Is the solenoid clicking when you turn the key to crank?
No click? Replace starter solenoid
Click, but no cranking? Check starter motor connections./Replace starter motor.

Starter?

bridge starter direct to start/check fuses.starter relay/antitheft remote control

Battery cables off the starter ,starter relay and ignition switch. these are the remaining items in the starting system for no crank and no start.
Get Shop manual and do the appropriate testing for each.

sounds like you need to relace the starter

hit the starter with a hammer a few times,if it turns over then replace the starter