The HDMI connection with the Mac mini fails. The monitor is going to sleep and never more awakes. At the back of the HP Pavillon PC - where the HP w2207h now is connected to, is present a DVI - I Dual Link (24 4 1) female connector. Is a >> HDMI<>DVI (24

This question doesnt seem to have anything to do with iCloud (the forum you've posted in)...

You'd be better off posting in the Mac mini forum, where people with relevant experience hang out:

https://discussions.apple.com/community/desktop_computers/mac_mini

I had my 2012 mini fail after 3 weeks, using both MDP-DP and then trying HDMI each resulted in a checkerboard pattern and couldn't get past the desktop, just constantly rebooting. I covered this in another thread about blinking, but to make a long story short, Apple told me that it's a known issue and only the Thunderbolt output to Thunderbolt is known to work perfectly. There is no current fix. Apple also does not allow a hardware replacement if your Mac dies from this, meaning they want you to settle for buying a new Mac and then not being able to use it unless you shell out another $1000 for a Thunderbolt display. It's ridiculous, and I see another person posting today they have the same issues, can't get a video output to work at all.