I dug through all my parts bins and found everything to make a working like-box ( Yay!). Some things could have been done in an easier way if I had the time to source parts somewhere. But I had only these parts, so this is the result.
Lots of people have asked me how it works and how it connects to the internet. Well, it doesn't connect to anything. It is basically a button connected to a display that shows how many people pressed the button. It's no more or no less pointless as the like buttons on facebook :)
Step 1: The 7 segment display.
The four digit display that I used was rated for 15V. But I wanted it to run on a lower voltage, because that was more convenient to me. So I desoldered the onboard resistors and swapped them for 10Ohm resistors. This lowered the voltage to 9V. Still to high to drive it directly with a microcontroller, but now I could at least power it with a power supply that I had lying around.