Animations not playing

I have an action in the dope sheet editor, I made a basic basic basic basic basic basic basic logic brick setup with a keybaord sensor, an and controller and action actuator, I selected the proper animation but when I start the game and press the key, no animation happens at all.

If you have a mirror modifier, did you apply it? It took me forever to figure this one out.
Make sure your Armature modifier is NOT applied.

No not a mirror modifier. But, I found it started working after I put the armature modifier first on the mesh.

I have spent so much time trying to fix problems and then realizing that it was a modifier that I hadn’t applied too. It’s annoying because it seems like a completely irrelevant fix.

It is irrelevant. It shows the current design problems between Blender and the BGE. While the BGE uses “parent armature deform” Blender was changed (quite a while ago) to use the modifier.

The BGE has very very limited support on modifiers (the same design issue). The BGE was changed to use Blenders deformation system (with Blender 2.62) which requires the armature modifier. Now you need both - the parenting and the modifier. The modifier will automatically be added when parenting. But have a look that it is the top modifier.