The firing pin(s) should be free to protrude from the breech face and able to move back and forth when the gun is cocked.
If by 'the right doesn't fire',,do you mean it won't drop the hammer when you pull the trigger (dry fire),,,or the right bbl won't fire a live round and give no primer indentation on that shell.
The former could be a problem w/the single (non-selective?) trigger which isn't all that complicated. It works off of the right hammer and sets when the gun is cocked. Then moves into position to lift the left sear when the right hammer is fired and falls.
The latter more likely a broken firing pin tip.
Not a hard job to replace. Most times the set screw that hold the firing pin are staked heavily into place and resist removal. Drilling them out and retapping takes care of that. But it's all extra work that can bring on other problems like a broken off drill or tap down in the hole.
Reassembly isn't hard with the right tool(s).
FWIW,,unless there is a NJ state law that requires you to ship a repair thru an FFL at your end to another FFL/Gunsmith,,there is no Fed regulation requiring you to do so.
There is no transfer of ownership on a repair. The FFL/Gunsmith is allowed to ship the repaired firearm back to the original customer at their home address.
Those companys providing shipping services can sometimes be the problem though as they tend to make their own rules when it comes to firearms and shipments.
