Hi,
Firstly, I think you would be better off contacting Zorin-OS support on this. There are many possible causes for this sort of issue. Having said that this is what I would try
1. Make sure the laptop is running the latest release of it's firmware. You will need to go to the manufacturers support area on their website. If this is an old/discontinued model, then they may have a separate web page for old/discontinued models.
2. I would try running Zoron-OS off a USB thumb drive to see if that works.
3. If it boots off the usb thumb drive properly then I would try installing each of the the install options starting with the "Core and Lite" option first, and if that works, then try the next and so on. Refer to the install guide on their website Install Zorin OS - Zorin Help
the idea behind trying the different install options is to see if the issue is due to some driver issue that is installed in a specific install option or if it's across all of the install options. If it's specific to one of the install options, then you can relay this to the Zorrin-OS support people who may then be able to identify the most likely cause and they may be able to tell you how to get around it.
Best of luck
Craig