"Hit & Run" and "Auto without Insurance" are different stories. You should have reported to police at the first spot. Right now, you can only check your policy to see if you have the "Comprehensive Coverage" option. But, anyways, you can try to contact police again if you have another party's license plate number, or discuss with your insurance company patiently....
Yeah, this is a tricky one. The key point is that if another vehicle is an "Identified" one.
If yes, like another party staying with you even w/o license, you will get "Direct Compensation" covered - most likely your premium will not be increased for "no-fault";
if no, like your case - even you didn't get the car's plate number, you will get "Comprehensive Perils" covered if you have that option - of course, deductible applies and insurance premium may be adjusted next year.
So, in a whole, try to avoid the "Un-Identified" conclusion if you talk to your insurance company after all it's not your fault. Insurance company may not care much as I think - hopefully they pay you simply through "Direct Compensation". You never know Good luck!
Keep a digital camera in the vehicle. Whenever this type of situation pops up, take a picture of another car as clearly as possible and then call police. DON'T CHASE the perpetrator, which may cause more accidents.
Call your broker or insurance company asap. If your policy is the basic, there may be a delay. If you've got full coverage, they will send you the check asap.