It's probably not the firing pin, but rather the transfer bar that is broken. There are schematics in the FAQ's that show the breakdown procedure. If you are mechanical you can do it. You will need some small pin punch's, and you will need to make a "dummy" or slave pin for the trigger group.
If you're lucky, you can find a transfer bar at Numrich gun parts, or Brownell gun parts.
Or, you can send it to H&R for repair.
When you press the trigger, there is a small bar that should come up and cover the firing pin, so that the hammer will strike it. You can, with the hammer back, push the firing pin forward to check it. I suggest it's the transfer bar, because that happens frequently, the firing pin not so often.
Good luck!
Ben