Can't find the noise

[FAST&CRAZY]

HI, New to the site and i would first off like to introduce myself. Name is JC and i have a 2005 cobaltss/sc.Now i have this noise which is a squeak and it drives me CRAZY. I took it to the dealer and they also hear the noise. It was there for just over three weeks and all this time they changed the steering column (that wasn't it) They changed the rear bushings (that wasn't it) They changed the lower control arms (that wasn't it)They checked the exhaust.(that wasn't it) They checked the heat shields(that wasn't it)So after all this time they released the car back to me and told me if the noise gets loader give us a call. Now i just went outside and gave the radiator a shake and noticed it seems a little loose as far as movement back and forth not sure if that's normal and also from under the car i pushed up on the radiator and it moved up . Does it sit in the lower mounts or is this mount broken. It's hard to see up in there.

 

[FAST&CRAZY]

Update on noise: Going under the car and messing with the radiator was a good thing. Took it back to the dealer and showed him what i was looking at and decided to put it on the lift. Low and behold wouldn't you know it the bottom mount had worn through and it was metal on metal. Turned the mount around to where it wasn't worn and the noise is gone. Ordered new mount and will be replaced by end of week. Better news is all previous parts added to the car are new and don't have to worry about them being replaced for a long time