There aren't a lot of options for a person trying to avoid paying taxes on a car. The state requires those taxes as part of the fee for registration. If you don't pay, you're flagged in the system as unable to register another car. The best thing you can do is get your taxes in order before attempting to register a new car, even though there are some loopholes in the system.
Contact your local Department of Motor Vehicles and ask what you have to do to register a new car. Don't mention the tax issues. If they don't mention it, you may be able to register a car without paying the taxes on another car, because it's handled by a different organization.
Transfer the title of your car to a relative or family member. Ask her to register the car in her name until your tax issues are taken care of.
Rent or own property in another state. Change your residency to that state, and register your vehicle there.
Talk to the people who handle the tax payments. Ask if you can set up a repayment plan and if they can lift the ban on your registering your vehicle.