Yes, assuming that the other person's insurance carrier accepts liability, they will pay for the damage to your car. I've posted a link below which goes into much greater depth regarding the issue of being involved in an accident that's not your fault while not being covered by liability insurance.
I am licensed in Nevada, but this answer should apply in California as well.
Unless there is a statute to the contrary in California, the fact that your car was unregistered and there was no insurance on it or boyfriend does not effect the whether or not the other driver caused the accident and should pay for the damages he/she caused. Open a claim with the other driver's insurance and demand them to pay for the damages caused by their insured.
Hope this helps.
/s Donald Kudler
Assuming the accident is not your fault, you should be able to get your car fixed and reasonable medical bills paid for. Unfortunately, you won't be compensated for any pain and suffering.
(Disclaimer: This information is not intended to be, legal advice, nor the formation of an attorney-client relationship)
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