2007 TL - New battery - when trying to start, no power at all, wait a few minutes then it will start. Thoughts? Thanks for any help.

I have an 04 Acura TL and my passenger HID headlight and fog light went out. It started flickering then totally when out. Had ballast/igniter replaced by my local mechanic. He ran a test on both lights and said they work but he is not getting power on that side of the car. The driver side works just find, could it be switch in the inside where the lights are being turned on? This has been frustrating and I need some help, please. Thank you!