se me duermen las manos y las piernas
My hands and feet are asleep. Probably referring to that tingling sensation when you don't get enough blood moving to the extremities. It works in English anyway. "My leg's gone to sleep" meaning you have been putting pressure on it and the blood isn't flowing fast enough and that tingle begins.
We visited the dentist today. After she injected the anesthetic, the dentist told us that she would wait for a few minutes for the tissue to "dormir". I asked if later it would "despertar", and she confirmed that it would. Apparently the terms "dormir" and "despertar" have the same context in Spanish as the corresponding words in English.
Their eyelids became heavy, they yawned and eventually their breaths became deeper and slower and they began to snore? My "legs fell asleep" is an idiom. It's literal meaning is nonsense. The likelihood of an idiom of one language having an "exact" parallel in another language is very small. If you want a "literal" translation, you need to start with an expression that has a "literal" meaning.