Seems like 3 things might be wrong. Too much oil. Not hot enough. Corn too dry. 3 tablespoons of oil, 3/4 cup of corn, very hot fire should do the trick.

What variety?

I grew strawberry popcorn this year and it pops with any oil.

In the past I have grown cutie pops popcorn and it only pops with peanut oil. This was extremely frustrating. I know that my experience doesn't make sense from a "how it should work" point of view, but you may find that using a higher heat capacity oil will make a difference.

There are usually only two reasons popcorn won't pop.
1. The moisture content is too high. If this is the case just let it dry some more and try it later.

2. It has crosspollinated with another type of corn. Nothing you can do except use it as an ornamental. Popcorn needs to be isolated.

It will also not pop if it's too dry. What causes the pop is encased moisture which turns to steam and the kernel quite literally explodes.
However, if it seemed damp but hard,it was probably not dry enough. The skin has to be hard enough to hold the steam inside until it explodes - try drying it out more.

Most farmers and grain handling elevators have moisture testers. I suggest you take some to have it tested.