hit by uninsured company truck

What is the name of your state? California (Los Angeles)

I was turning left in the left-hand left turn lane; I turned the corner to the next light and sat motionless. A large company truck was turning left in the right-hand left turn lane. I noticed the front of the truck come inches from the front passenger door/right fender of my car, and the next thing I knew, the rear part of the truck was up on top of the right side of my rear bumper. The bumper sustained damage. I got all of the information off of the truck (company name and number, truck #, CA #, DOT #, license plate). The driver informed me that he worked for an agency which was contracted by the company itself and that the truck didn't have insurance. I have insurance, but my registration is on hold until I pay a $300 ticket. I have already paid for the registration through AAA, and my insurance is valid. What course of action should I take? We did not file a police report because I wasn't sure what would be said of my registration, and because LAPD would never have showed up anyway (I've been involved in similar accidents in the past, though I was never at fault). What are my options?

I don't understand your accident description, but you can file a claim under your insurance policy's UMPD or collision coverage. You will be required to pay your deductible.

If your insurance is valid, they will take care of you and then subrogate against the company. I find it highly suspect that a commercial carrier doesn't really have insurance. I suspect the driver was just ignorant.

The status of your registration shouldn't affect your insurance, but you dodged a major bullet as the cop could have charged you on that count. When your vehicle is unregistered they expect you not to drive it no matter what lame excuse you have.