Live in California, my car hasn't been registered since '04, no non op?

Another wrong response.
Once the car goes several years without being registered, it is dropped from the system. To register it now, it is as if the car never existed. There are no back fees to pay. You will need to get a VIN verification, pay transfer fees (Even though YOU are the last owner) and sales tax. I have bought "yard cars" that people bought and let sit for years. Almost every one of them was unregistered for10 years or more. EVERY time I called DMV to check status, they told me that the vehicle is no longer on file and will have to have a new file created.
It isn't as easy as re-registering but you are in no way screwed.

This hasn't been true since the late 90's when everything was converted to digital. It used to be that cars dropped out of the system after 7 years if they weren't registered. Since the registration system has gone digital there's no need to physically store actual paperwork, and so the digital records stay on the books. And yes, I've encountered the exact same situation as the OP with a car I stored for over ten years in that time. I've also bought cars in that time that were unregistered for over 7 years and had them still be in the computer, a royal headache in one particular instance because the owner of record was not the person I had the bill of sale from. That was not fun.

As far as the OP's car goes, you're going to have to go down to the DMV. In some cases you may be able to work around paying all the back fees. For example, if it's a project car that's been in storage and hasn't been driven or parked on the street, you mayto be able to talk the DMV into filling out a statement of facts regarding the storage and the back fees can be waived. But, that's not a 100% sure thing, it depends a lot on the person you get at the window and them being willing to work with you. I have absolutely done it on cars I have purchased, and even one that I was storing long term that I let lapse.