Well wlf,
I think that you can rule out the shells being the problem. If you can put the unfired shells in another shotgun and they will fire, this means that your savage single shot is the problem.
I would have to assume and say that even though your firing pin is hitting the primer, chances are the firing pin is probally weak.
After all, when the primer is struck and ignition occurs, it will ignite the gunpowder causing the bullet to exit your barrel.
If it was bad primers......the shells wouldn't fire out of any gun.
If it was bad powder...... the shells wouldn't fire out of any gun also.
Your problem is that the firing pin is not getting a good enough hit on your primers.....this is probally due to a weak firing pin or a chambering problem.......but I doubt the problem lies in the chamber.
here's a link that might help you,.... but if you dont think you can do this yourself, you should let a competent gunsmith check it out.
http://www.brownells.com/aspx/ns/store/productdetail.aspx?p=16336