Friday Inspector failed my car:
!. Led headlights. Va law states automobile must have same type lights as factory installed. Ok I installed halogen bulbs
2. Fog lights not working. Yep running lights or low beams must be on for fogs to work. I forgot about that until yesterday
3. Battery not secure Bottom bracket was on and tight don't know what he was looking for I couldn't move batt.
Damn this pisses me off especially headlights . Going back tomorrow for reinspection.

 

Good luck - strange that he dinged you in the battery if it was as secure as you say. The wedge at the bottoms of the battery is all that secures it in place.

 

He may have assumed that a hold-down bracket was missing. Might have to show him a picture from the service manual showing that the C5 does not have a top battery bracket.

 

I live in VA, and I've never run into these issues. I was running LEDs in the stock housing for awhile with no issue (passed inspection at 2 different shops). I currently have HID bulbs in an ACA housing. I have not had any issues with that either (in fact the same shop that does my inspections is the shop that aimed them for me after I installed them!). I also have LED side markers, and tail lights. I actually called and checked with the state inspector at my preferred shop before I ordered these lights, and was told that as long as they were the correct color, there would be no issues at all. All the lights do have to be DOT compliant. However, there is nothing in VA law that says you can't have aftermarket lights.
If your fog lights are functioning, and the inspector couldn't figure out how to make them work...that says something. Plus, considering that not all C5 Corvettes even HAVE fog lights, I'm not actually certain that they need to function in order to pass inspection (all of your other lights certainly need to be working though)
Also, I've looked and looked, and I can't find anything that says your battery has to be properly secured as part of the VA state inspection process. You'll need to get your car through their inspection. However, I don't think your shop is reputable. They're just trying to take you for whatever they can. There can actually be a shocking amount of stuff wrong with a car that can still pass a VA state inspection. Once the car is re-inspected, I would never go back to that particular shop again.
You might want to ask their inspector to show you what part of the VA inspection code says that the various things he failed you on aren't allowed. Any reputable state inspector should be able to do this. I had this happen to a friend of mine several years ago. They gave him a long list of things that caused his car to fail inspection. When my friend asked to see proof that all of these things were needed to pass inspection, they backtracked and admitted that only ONE of the approximately 12 things they listed was actually required to pass inspection, the others were just things they(the shop) recommended.

 

Sounds to me like you got an inspector having a bad day and just looking for someone to **** on. Ran into this a few years ago when I was in the impala club. Mildly modified car (aftermarket exhaust and intake) and the inspector was goosing the throttle on the dyno trying to make it fail the tailpipe sniff test. We called her on it and reported it to her boss. He chewed her out (apparently she had done this before) and apologized to the owner of the car.