I too, have problem with the micro-hdmi port:
I have bought a hdmi micro converter (micro to normal hdmi). When I use it with a hdmi cabel, there is no reaction to the screen attatched. I have read that other people have been cutting some of the plastic off their micro hdmi converter stick. See here Hanselman:
It turns out that many cables (especially cheap ones from Amazon) don’t expose enough metal to make a decent connection.
Take a razor blade and cut a good millimeter around the cable’s rubber housing to expose more metal.
So far, I did not try it myself, as I would like to test with other cables first…
Go thrugh this first (drivers):
2.99£ – but maybe only shipping in UK (free).