How to start an animation at a different frame than that of the start of the loop Is it possible in the Blender Game Engine to start an animation at say frame 1 and end at frame 20, but after the first playback to start looping frames 5-20?
Try this: 

It starts one animation and plays it once from frame 1 to 20. Once that animation reached frame 20 the actuator isn't active anymore. This means that if you set up an actuator sensor to a Nand controller to a action loop frame 5 to 20 it will work.