Ghorpm: Yes, it's RPG and it's a standard fantasy-medieval setting with a few sci-fi elements
Might and Magic 7, golem collection.
It came to my mind when you mentioned body parts, but I dismissed it because building the golem is in no way crucial and hardly something that has to be done quickly. Plus, I was under the impression it's an adventure.
The sci-fi elements reminded me of it again. And now I understand what you mean about having to do it quickly. Building the golem has a nice side effect. "Promotion" and all that. 4 mages in your party? Or 3 mages + cleric?