Wow - that's a nightmare! I'm with Jerry, stuck rings are usually "stuck for a reason" and in the great scheme of things, rings are one of the least expensive components. I'd be concerned that you have a bad piston (or two?) if rings are not nice and springy when inserted in the cylinder.

As mentioned, bad intake gasket (usually pinched) can allow vacuum in the lifter galley.

Some additional information, re; what are you working on and is this something that you just bought or do you have/know the history of the engine?

Good Luck,
Glenn