Auto Insurance Claims: Salvage Title, honda civic lx, salvage title

Question
I have a 2001 Honda Civic LX that has a salvage title. I have full coverage on it since I bought it (4 years a go).
Two weeks ago, I got hit by a deer (Driver and back passenger sides). I called my insurance and informed them with the accident. Took my car to a body shop and the estimate they gave to repair the car was: $5,200.00.
My insurance told me that my car is totaled loss. They offered me $3,900.00 as settlement! I refuse to accept the offer because I was paying insurance coverage like a normal car (with Clear Title. The Insurance told me: Did tell us that you car has a Salvage Title? I replied I gave all the information you have asked for (Vin#...). what my options:
-Can sue for charging more then They suppose to?
-Should I keep the car I repair it since my car runs great and well maintained?
-Can they say NO once I repair the car and ask them to reinsure my car again?
Please comment.

Thanks.  

Answer
The exact answers to your questions vary from state to state, policy to policy and company to company, especially regarding the retention of the salvage.
Generally speaking, the insurance company owes you the value of the vehicle regardless of the premium dollars paid.  If they had known of the salvage title, it would not have resulted in a lower rate.  It would have resulted in no coverage at all beyond Liability and UM.  You should consider yourself fortunate that you slipped under radar and retained the coverage that you did.  Let's say that instead of salvage title issues, you had issues regarding prior, unrepaired damage.  They would be within their rights to subtract from your total loss settlement; a significant the cost of restoring the vehicle to an undamaged condition.  Let's say that a tree fell on your car when it was sitting in the driveway with a blown engine.  If they know about the engine, they are within their rights to subtract a portion of the cost of engine replacement from the settlement.
Settlements are not based on the actual cash value of the vehicle at the time of the loss.  A salvage vehicle is worth only 50-60
s much as a non-salvage vehicle.  I'm sure that you didn't pay full price nor does the insurer owe full price.  
Because there is so much fraud involving people attempting to insure salvage vehicles for their normal value, insurance companies will not generally write full coverage if these facts are disclosed.  In fact; you may see language regarding this subject on your original application for insurance.
Again, you are fortunate that any coverage was afforded at all.
Good luck.