It sounds like you have previously had insurance on the salvaged vehicle. So it is possible to insure a salvaged title in NJ but the type of coverage you are able to obtain might vary from insurance company to insurance company. Generally it will be possible from some insurance company to get liability on the vehicle but collision and comprehensive might be more difficult to get.

It appears the insurance company paid you the current value of the vehicle at the time of the loss. Typically salvaged vehicles lose as much as 50% of their NADA or Blue Book value. If you ask the insurance company how they came up with the amount they paid out I am sure they would supply you with the information they used to calculate that amount.