DoubleD,

I believe the serial number will not be on the barrel but on the action. or at least, I have not seen a serial number only on a barrel.

Sometimes they are on the face or bottom of the action and other times they are on the lower tang.

"It did not shoot very well." Many vintage guns having been shot with black powder and corrosive primers have poor bores. Some can be cleaned up by lapping which is actually not hard, just time consuming.