Which USB creation tool did you use to make your ZorinOS installation USB?
Did you check the SHA256 checksum of the ZorinOS Core downloaded .iso file against the published value on Zorin website.
FYI. Some basic installation advice can be found in this thread: Before you install
If you have completly wiped the hard drive and the Live USB runs OK on your machine, I guess you could again try to install ZorinOS from the USB.