What GPU? Nvidia? Try updating drivers? Which GPU model exactly?
I believe Zorin keeps updating kernel so GPU drivers may be out of date (not compatible) with latest kernel or something like that, especially nvidia.
BTW, any reason why you chose Zorin? It looks kool but I'm not a fan...
Have you tried something like neon.kde.org or elementary.io ? (Both also ubuntu-based and pretty nice, they are my favourite distros)
PS: elementary.io download asks for money but you can click "custom" and enter zero to get download link without having to pay anything.