Here's the deal, I have a Remington 597 and i love it but our relationship started rocky.
The first thing you should know is the fatal flaw of the 597 is the extractor, it sucks and it basically ruins the gun. Makes it so bad functioning you don't or won't want to shoot it. The GREAT news is Volquartsen makes an AWESOM AMAZING extractor for $20 bucks, and replacing it just cannot be overstated how a difference it makes on the overall shooting of the gun. Further they make a $40 "target" hammer for the gun, again just completely revolutionizing the operation and shootability of the gun ... for $20 and $40 = $60, and its just an amazing upgrade.
That admittedly would not explain why it just doesn't go bang... Odd. What ammo are you using? Because Remington rimfire ammo sucks... and I mean sucks. I bought my 597 and a few bricks of Remington golden bullet .22LR as my first long gun, and I had such a terrible experience I almost threw the thing in the garbage. After some upgrades and throwing the Remington AMMO in the garbage and getting me some CCI< my 597 is now my favorite amazing rimfire.
here is my baby now:
Basically, it was the Dick's Sporting Goods combo rifle , a OD Green synthetic stock'd 597 with a cheap "Remington" 3-9x32mm scope. Replaced the extractor and hammer with the Volquartsen Edge Extractor and Target Hammer, the scope with Nikon ProStaff 4-12x40mm Nikoplex scope, a Winchester 9-13" sling stud bipod, Uncle Mike's sling studs and sling swivels, 1 1/2", a military contract silent sling, and then the stock with my lol custom paint... Used me some 4 different colors of Rustoleum Textured Finish spraypaint to do a little camo shading. Its unique LOL :-)
anyway, try those two VQ parts and CCI or Federal ammo...those are the two my 597 will eat.