Savage 24 Combo Gun Fails to Fire 22lr

I just got my Savage 24 combo gun with 22lr / 20g. It's a pretty old gun I got off gunbroker. Unfortunately, I've been experiencing a lot of failures to fire.... about 1/3 of the time it fails with a wide variety of ammo. On failed fires, the rim impression looks pretty much the same as successful fires. I'll upload a pic if I get a chance. Does anyone have any advice?

I'm thinking about:

1. Replacing the Mainspring
2. Replacing the .22lr Firing Pin
3. Replacing the Firing Pin Spring