I have been trying to install the damn link pin on a new barrel and I cannot get it to go in. The pin is sized properly but it will not go in. Has anyone had this problem and how did you solve it?

First take a micrometer and verify OD and ID dimensions of both pin and the holes in barrel lugs and link pin. Then take a fine grit stone and very slightly "break" the edge of the link pin so you have a VERY SLIGHT bevel on the end. If you have a vice start the pin in the hole and very gently start the pin in a mm or two till it is just shy of the inside edge of the first lug. Continue to drive the pin in bit by bit till it is fully seated through the link and both lugs. Remove barrel and using hammer and punch and a third hand holding the barrel on the flat on the vice drive the pin in till fully flush on both sides. If necessary you might need to file the ends of the pin on the outer sides of the lugs for it to fit in the frame without any resistance. Assembly should fit and move in the frame freely without any wobble.

Chuck the pin in a drill or drill press and use sandpaper to polish it. Switch ends and polish again.  When you can start it into the hole with a light hammer tap, use a pair of smooth vise jaws to press it fully in.  The pin should be tight enough to not fall out but loose enough you don't have to beat the hell out of it.

This.  Press it in with a vise.  If the pin winds up being a little loose then peen the pin ends with a center punch.

Sorry Marleybob, gotta disagree with you on this one. Not trying to bust your chops on this.
If the pin ends up through the two lugs and the link, AND is loose enough to need peening, start over with a new pin and proceed a little more slowly so as to not remove too much metal. I was told by the smith that taught me that a peened pin was the sign of a man in a hurry. The gun will likely run ok, but just depends on how much the details and workmanship matters to a person. ymmv and jmtcw.