Okay then, maybe there was some confusion.
As far as Aquinas goes, I think there's reason to believe he didn't make a fallacy of composition in his prime mover argument. I'll provide here a rough distillation of the argument:
1. Some things are in motion.
2. Nothing can move unless it first has the potential for that movement.
3. It is an act, when motion occurs.
4. Motion is the reduction of something from potentiality to actuality.
5. Whatever is in motion is put in motion by another.
6. A thing can only be put in motion by something in a state of actuality.
7. A thing cannot be in potentiality and actuality at the same time in regards to the same type of motion, but can be in regards to different types of motion. (Something that is actually hot cannot be potentially hot, but it is potentially cold.)
8. Therefore, it is impossible for something to move itself.
9. Since a thing can only be put in motion by something else in motion and that thing too must be put in motion by another, and that by another, then there must be an infinite regress of movers moving things or there must be a first mover put in motion by no other.
10. An infinite regress of movers would have no first mover and, consequently, no other mover, since subsequent movers move only inasmuch as they are put in motion by the first mover.