Here is a step by step tutorial to make a functional lego case for your Samsung Galaxy S4-Mini.

The buttons are handled by lego technics parts, and this case will protect your cellphone just like any other one; the only limitation for now is the back LED which is hidden and cannot be used for anything else than give a nice red glow.

I deliberately picked strange and colorful parts to give it a patchwork look, but of course you can take whatever combination of colors you want and decorate it at wish.
Another particularity is that the two faces of the case are 'positive' legos (so the moving part is not hitting the phone's screen).

Step 1: Bottom Case: Basis

This is quite straightforward.

The last step shows decoration parts (but I encourage you to put something in bottom right corner so the case will be stable).

Special/strange parts:

The old red car part can be replaced by a combination of four 4x1 and one 2x1 parts.

The black T (which is a broken car part) can be replaced by a 2x3 part.

Step 2: Chocks and Button Handlers

Here you will need some lego technics parts.

Pay good attention to the orientation of the parts if you want the buttons to be activated correctly.

The red button will not fit exactly because of the 2x1 chock on the other side of the brick, but that's ok.

Step 3: Bottom Case: Sides

Start by flipping the case so you see the 'negative' side.

Here you will see if you set the buttons correctly :)

The cellphone must be 'naked', the battery will be in contact with the back of the case.

The chocks and four 2x3 parts on the top are there to keep the cellphone enclosed; it has to push gently on its surface, so if you feel a problem check the previous steps for possible errors.

Step 4: Top Case

Finally we can construct the moving part that will protect the phone's screen.

Once again, the last step shows decoration parts.

Special/strange parts:

The top triangle is here for balance, the bottom triangle can be replaced by almost any part.

The blue 2x2 bolt is a broken seat, it can be replace by an usual 2x2 part.

Step 5: Final Assembly

Put the top and bottom case together. It may not fit perfectly at first so do not hesitate to push it here and there, after a few manipulation everything should be ok.
I hope you enjoy the new design of your cellphone :)