There is a way to get the serial number "put back." Gunsmiths and engravers do it all the time.
The simplest thing to do, since the serial number does exist on the gun, is to have a gunsmith re-stamp it on the frame.
I strongly suggest that you contact the nearest office of the Bureau of Alcohol, Tobacco, Firearms, and Explosives. Write a letter detailing the entire story, including where you got the pistol, and ask for guidance. Explain that you are already in contact with the State Police about the matter. BATFE will be very helpful.
Meanwhile, ask your State Police contact to check whether the gun was stolen or crime-related. If it is stolen or otherwise related to a crime, be prepared to lose it without regrets.