How can unpopped popcorn kernels be used? Can they be composted?

Sure. Lately we've been munching on pistachio nuts, and putting the shells in our compost. Some suggestions for alternative pistachio recycling may also apply to popcorn kernels:

Use them at the bottom of plant pots to help drainage.

They can be made into rattles (in an old tin can or cardboard tube)

Spread them around the garden – eventually the kernels will break down into compost and feed your soil.

Of course you can compost them, they are plant material. If you want, you can put them out and see if any squirrels or birds would want them.

If you do yard composting, dig a hole and bury them with other plant material, napkins, and bones. If you have a compost bin, put eggshells, bones, greasy pizza boxes, paper plates, paper towels, fruit peels, and your kernels with leaves, branches, and grass clippings.

They most certainly can be composted,quite as anything pretty much organic.

You may also make use of them a bird feed,or some kind of feed to some pet(by soaking,if necessary).

Another alternative,you might be able to make use of them,say,in decorations,such as some kind of handicraft!

I'd go with either compost or bird/squirrel food myself.