I have a 2007 HHR. Thought the starter was gone as when I started it all it would do is make a whizzing or zinging sound. I bought a new starter put it on and am still having the issue. The starter will not engage to turn over the car.

 

That description sounds sadly like a stripped fly wheel.

 

Welcome to the site, check the under hood fuses and the battery connection in the spare tire well in the back, also check or have checked for you the battery condition.
It is possible your battery has given up

 

When you removed the old starter, did you find the gear on the end that engages the flywheel was all chewed up, or more likely badly worn? If so, it would indicate that the teeth it engages on the flywheel MAY be the problem.

If you remove the starter you should be able to have a look at the flywheel teeth - you may have to use a mirror and a flashlight to get a good view.

Here is a good video on diagnosing starter issues, from the battery itself onwards:
and here is a video of what damaged/worn flywheel teeth look like: