Can I sue for remainder of my car payments if a person hit and totaled my parked car?

No, you can't. The law does not use the cost you paid or the amount you still owe on a car as the measure of what you are entitled to: it uses the value of the car. If you received an amount at least equal to the then-current fair market value of car (it's "blue book" value) as of when it was totalled, that is all you are entitled to; you cannot sue anyone for more money. (If you didn't get this full value, however, you should be able to sue for the shortfall.)
You can see why the law uses value, not cost or amount owed, by considering the following: say that a parent buys a car for his/her child, or  a spouse gets a car in a divorce, where the other spouse had paid for the vehicle. In these cases, the car's owner has not paid anything for the car. If the law used cost or amount owed as the benchmark for compensation, the child or ex-spouse would get nothing if their car were totalled, since they paid nothing for it and owe nothing on it. Clearly, that is not a result society or the law wants. 
Cost or amount owed varies so much--did you strike a good deal or a bad one? Did you pay cash up front or finance? Did you have a trade-in? Did you buy during a President's Day sale or year-end clearance? Was the car a gift? Etc.--that it can't be used as the measure: it is too variable, too inconsistent, and too subject to being manipulated. So value, not cost or amount owed, is used.