Well, I bought the digital copy.
I started it up and it said:

We have detected the your video card is not supported by Diablo III
Operating System: Windows 7 Serivice Pack 1
Video Card: Mobile Intel (R) 4 series Express Chipset Family

...

Does this mean I need a new gaming computer with a good videocard?
or is there a way I can fix it so I can play it?

This is a bummer