Humidity can damage more than your pantry. Mildew can damage just about everything (I have too much experience with this)
, and some molds may even be a moderate health hazard.
Tackling dampness and mildew in the basement should be a high priority. Bonanacrom is right, but if that's too big a project, at least buy a couple dehumidifiers.
Do some research, use them properly, and you might be amazed at how pleasant a space your basement can become.
Bottom line: Rather than approaching this as "protecting your food from moisture", approach it as a full-on attack at preventing the moisture to begin with.
Locked, but left here as an example why the PAW will suck beyond imagination. You people can't even get along when there isn't stress and starvation. Imagine what a bunch of raving lunatics you'll be when you have to skip a couple meals and wipe with the Sears catalog.