How to connect a 23" Cinema display to my Mac Mini

This display is DVI-D and I don’t have the original power supply, It was working when I bought it, I saw it working and has no problems.

I’ve now have bought a Mini DP to DVI adapter to connect my Mac mini which only has Mini DP port. I can't see pictures appear on the 23” Cinema display,

I want to know what's wrong, is the problem the Mini DP to DVI adapter?

Thanks!