Woofie, that was my 1st question as well! I've learned that once my seed packets are open, the best way to store them is in an airtight container, put into the crisper of my refrigerator. I've had pretty good luck with this method.
You could try the damp paper towels to check your germination rate, but I've never tried to start my seeds that way.
Maybe someone with more knowledge here will chime in!