REO Mini Update. Once again, I cleaned my firing pin with alcohol and a q-tip, moving it up and down to clean as much as possible. I also used a damp alcohol swab around my button. I let it dry for an hour or so. Then I q-tipped with Noalox both on the pin and the battery, moving it up and down and let it sit all night. This morning it seems to be working okay. I think my REO may need regular applications of Noalox. Either that, or my firing pin got all gunked up and needed cleaning.
So, thank you folks for all of your help. I hope I don't have to come back with this particular issue again, but if it should happen, I know there's lots of help here.