Gunrunner, is this a hammer gun? If it is it is likely a grade 0 or 1. They were the lowest grades of Parker hammer guns. The grade 0 usually had no engraving on the sideplates except the Parker Bros. name and the grade 1 had a bit of border engraving. They usually had plain twist, twist, stub twist, or laminated barrels. The books say laminated barrels weren't used on 0 grades, but that is wrong as I have one that lettered as original. The rib had the type of barrels engraved on it. The twist and plain twist were the same steel, just sometimes they didn't engrave the word plain. Stub twist was made from the stubs of used horse shoe nails. It was believed that the constant hammering of the horse's hoof improved the quality of the steel and it was considered a higher grade than plain twist. The twist, laminated, and damascus barrels were made from strips of iron or steel called ribands that were hammer welded around a mandril to form the barrels. Laminated barrels had a higher proportion of steel ribands than twist barrels and was considerably stronger. While they were wrapping the ribands of the damascus tube they twisted (braided) the ribands as they wrapped them around the mandril which gives it the nice damascus pattern. The Birmingham proof house tested many types of barrels for strength around 1887 and the fine English laminated barrels were near the top with Whitworth steel. The Belgian laminated didn't fare as well.
If it is a hammerless gun it is likely a PH grade, the lowest hammerless grade with composite barrels. The next up hammerless grade was a GH which usually had what they called D2 damascus. The numbers went up with the grade and quality of the damascus, DH were D3, CH were D4 though they often had Bernard steel barrels (a different type of damascus), ect. up to D7 on the top grade.
Until Whitworth patented his compressed fluid steel process the fluid steel of the time had some small air bubbles trapped in the steel which weakened the barrels. Quite a few failed during proof testing. I think his patent was in the late 1860s though the barrels weren't available for several years after that. Whitworth steel was only used on the top grades of Parkers.
As for value it depends on condition and the type of gun. Value is much higher in the U.S. than in Canada. Parker had top lever hammer guns as well as what they called lifter guns. The lifters are an earlier design that had a part in front of the trigger guard that was pushed up to break open the barrels. I'm not an expert on either Parkers or composite barrels and someone may post some corrections to what I have said. It would be interesting to see some pictures. Post or pm me with the serial number and I should be able to tell you the grade, year manufactured, and original configuration of your gun.
Bob