The material in the matches is a decent dessicant- your Ohios are going to be a bit older, they haven't been made for a while. So they've probably absorbed enough moisture out of the atmosphere to render the tips inert. Damp proof means they can take a little moisture, but without being an air tight container or given a coat of shellac, they've sucked too much water out of the air.
I buy the Diamonds when I find them, then I dip them shellac, two layers, and store them in an air tight container. I've got some Ohios that are ten years old that I did this with and they light up pretty regularly but even with the moisture proofing they are getting flaky enough to retire to woodstove detail.
As for a striker, try a metal nail file. I also cut a strip of striker off and tape it to the inside of the match case, facing the sides of the case. But since I don't like being cold and wet, I always have a lighter or two and at least one ferro rod along with at least one match case.
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-IronRaven
When a man dare not speak without malice for fear of giving insult, that is when truth starts to die. Truth is the truest freedom.