Mac Mini Mid 2011 fan At full speed although says 0rpm

Sounds like someone broke a component on the logic board when they were in the system.

The logic board has a small section sticking out at the front of the board (you take the board out from the back) which in the process of installing can snap off one of the components. The part is part of the fans tach logic has come off or the fan socket was damaged (on the far left in the image)

Take the board out and compare it to this image: Mac Mini Logic board.

Does it look OK?

To take the logic board out follow this IFIXIT guide: Mac Mini Mid 2011 Logic Board Replacement through to Step 17.

As the drive and its cable is missing you'll need a few parts. I would recommend you get this kit: Mac Mini Dual Drive Kit just get the kit without the tools if you have them. That way you'll get all the needed parts to put in a drive (just ask for the lower bay - primary drive cable instead)