Long story short, I live in Anaheim, CA. I can't find any mention of laws regarding this, so here goes. My father has had a classic Camaro in our driveway since the 90s. It has been parked and rusting away. It is insured and registered as inoperable, since it doesn't run. I now have the means to fix it for him, so I've been working on it here and there in the driveway. The city came to my home and gave me a warning that I need to either finish and get it running, or they'll tow it away? If I just cover it up with a car cover will I be fine? Or, do I seriously need to get this thing running in 3 days? Are they even allowed to do something as extreme as take the car from us?
Yes, in Orange County, CA, in a residential zone or on residentially-developed property, this is a code violation. Specifically you are looking at Title 3, Division 13, Article 1, Sec 3-13-4(11):
Sec. 3-13-4. - Prohibited Conduct.
Except as provided in section 3-13-6, exemptions, it shall be unlawful for any responsible party having charge or possession of any real property in county territory to:
(11) Keep, store, or maintain upon any premises under his/her control any abandoned, wrecked, dismantled, or inoperative vehicle, or part thereof, except as permitted by Table 3-13-6(c).
You may store/work on this vehicle from a building or location that is not visible from the street, but you cannot work on or store the vehicle on the street or driveway. You might also be able to erect a 6' tall opaque fence around the car, provided the fence meets standards.
The code making this illegal is a county ordinance for Orange County, CA, which is not applicable to other counties in California (other counties/cities may have their own ordinances). Codes which cover this sort of activity are generally made at the county or city level. They vary dramatically from location to location, and are often different based on the zoning of the property within the county or city.