2005 cavalier when i give it gas to go it makes a grinding sound ????????????

Did the anti-theft light come on when you replaced the battery?

https://www.google.com/search?q=2005+cavalier+theft+system+reset

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is the emergency brake stuck or on ?

Hi Gallen, Take the vehicle for a diagnostic scan. I believe that if the problem is evident only when starting from cold there may be a problem with the cold start operation. The scan will pin point the problem. Regards John

sounds like maybe your wheel bearing is going out

cv axle..replace them both

This sounds like the starter if its a grinding noise, you will have to replace the starter, which is about $170.00 with the old starter core turn in at the auto parts store.

Could be wheel bearings . Some times they make noise at certain speeds. Even had a vibration with a tires out of balance. I had to get new tires.

it might be your transmission.

This sounds like a broken motor or transmission mount.  Try to isolate the location of the banging noise to give you or a mechanic an idea of which mounts to check first.  Some motor and transmission mounts can be tricky, so you may have to remove them to see that they are worn or broken.