Hi Dan,
Based on the serial number you provided, it looks like you have a nice 16ga DH (Grade 3) Parker which should have 28" barrels according to the serialization book. Your Dad has passed down a very desirable Parker which you should be proud to own! I live in Raleigh and would be happy to look at the gun for you. I can also make a recommendation for a gunsmith somewhat close to you that could check the gun out for safety prior to shooting it, if that's what you're interested in. I'd call Ken Barfield at Double H Gunsmithing in Blanch, NC.
http://doublehgunsmithing.com/ Ken isn't as close as the Gunshop down the street, but he has good knowledge of older doubles, and has done some small repair work for me in the past.
If the gun is in good condition, it shouldn't take much to care for it. I'd suggest purchasing some low pressure shells from RST (
http://www.rstshells.com/) and getting her out into the field or onto a sporting clays course!
Mike