Rode the cart but don't have enough mechanics to open the workshop--no place to go (except the trapped room). What's next?

There's a key for the workshop on a body you can get to fairly easily.  Be careful though.  If you want more specific than that, say so.

The mine ride just takes you to a secret room with some extra treasure. It is an entirely optional area.

 

Here is a map of the level. There is a seal in Room 1, that you use to open the door to Room 7.

Thanks, People! That's a great walkthrough--I was looking for one. Mostly I stumble through, miss a lot.

Heh.  I stumble through the first time.... THEN I find a walkthrough so I don't miss anything for the rest of the playthroughs!