Just a suggestion, but maybe you should download and burn an iso disc of ubuntu 12.04 and try installing that first....if that installs properly, then it should be easy to switch to zorin by then having it wipe out ubuntu and re-install with zorin if you prefer...
Any time i got a new computer, i always had 100% luck with wiping out windows and the grub being set up properly with the new ubuntu system...
just a thought...you could try!
As far as Zorin goes, if you could get the actual ubuntu installed, you might want to just leave it on for a while and then wait for Zorin 6 to arrive (which should be very soon, actually)...
In fact, i am currently running ubuntu 12.04 with the Cairo Dock session w/unity panel (gives you the nice global menu but without the unity)...when you install cairo dock on ubuntu it sets up several log in options on the log-in screen automatically...
Using Ubuntu 12.04 w/cairo dock for me is almost as nice as running Zorin (no offense to the "Zorinites" here)
So, you might play with that for awhile if you can get that going while awaiting for Zorin 6 final release...