"I am sure some would cringe if I asked "could it be re-blued, with new internal parts, and shot once in a while?"
It's definitely shabby but I'd love to sneak up on an old revolver just like it and be able to give it some tender, loving care and provide it a home.
I'd be one of those returning it to shooting condition. It isn't something that I'd want shoot regularly but it would be great to hear it "speak" again and know that it could. Parts are available to cure the ills you mention though gunsmithing on early Colts isn't cheap. Most of the internals are fine and probably only a couple of parts are needed to get the revolver going. If you're really clever you might could get it going yourself with time and much patience.
It even could be a candidate for refinishing. It is currently in such poor condition that a refinish wouldn't negatively affect its value. Roll markings on these models weren't very deep and may become obscured by rust or excessive cleaning. Sometimes though, a careful cleaning and polishing in preparation for rebluing can reveal markings still intact though weak.
Cost of refinish will be more money than the revolver is worth but the cost can become a labor of love and the restoration can be a fun hobby all its own. There are professional restoration specialists who can turn that sow's ear back into a silk purse if your own purse is deep enough. Original type blue, roll markings restored, correctly case hardened parts, fire blued hammer, trigger, and screws are what is called for in the case of a restoration. Even those guys can't fill the pits in that original barrel though.
While it is a sure bet that your revolver's bore is impaired, sometimes they are relatively unscathed and quite shootable. That revolver gives every impression of having been left in a barn or tool shed, subject to temperature variations and humidity over a number of years and the bore has to be suspect.
Take a look at the .44-40 from this auction.
Colt New Service 44 40 Fair condition : Revolvers at GunBroker.com
This one is very similar to the New Service you feature here. There is less difference in condition than might meet the eye at first glance. The one in the auction has been heavily cleaned (too heavily cleaned in my view). At some point in its life it looked much like the one in your photos. The pitting remaining on its surfaces is the result of heavy rust that has been cleaned away. Note how only a ghost image of the trademark Colt logo may be seen on the left side of the frame and note the caliber roll marking on the barrel. This would very likely be the same style of markings as would have been found on your friend's gun. The auction New Service has an incorrect ejector rod head and the front sight has been monkeyed with. The hard rubber stocks appear to be original to the gun. Someone "thoughtfully" mutilated the left side of the frame with crudely added initials. There's a good chance that the crane was pried on in an effort to open the cylinder when this gun was still in its rusty state as indicated by the marks on the inside of the frame.
Twaits' valuation of your old Colt is good. It would be worth perhaps twice that if it could be put back in good working order. Don't allow the starting price of that auction to unduly influence you. That is only a figure and not a ironclad statement of value.
Personally, I'd prefer to own the old rusty New Service rather than the one in the auction.