As it stands your board needs a BIOS update before you can install your chosen processor - Do not attempt to install the i7-3770 processor yet.
You've already identified the AA number on your board G10217-303. The number at the end is less than 304 so the board will not have been produced with a high enough BIOS version for 3rd gen processors.
The number at the end is 301 or greater, so the hardware on the board will run your processor when the BIOS is corrected.
You will need a Sandy bridge processor which is on the boards compatibility list for your existing BIOS version (I used a cheap celeron) to do the necessary updates. You can probably identify the existing BIOS version by looking at the other documentation about the board (Tech prod spec maybe - can't remember off of the top of my head)
Caution.... Read and follow the flow chart on the PDF very carefully - do not rush or skimp - read how to do F7 and recovery flashes - again be VERY careful not to deviate from those documented processes.
Good luck - flashing these boards is very dangerous even when done correctly. I have had terrible issues with i7-3770 and DZ68BC.
For anyone experiencing DejaVu - you're not going mad, this post IS a rehash of one I wrote about a week ago!