Trying to install Zorin OS 15.3 lite (latest) on an old HP 530 notebook. Running from USB works like a charm, but after clicking on the icon for the installer the language selection appears for about 1 or 2 seconds and then closes without any further error message.
If Windows is currently installed on the drive, ensure that Fast Startup or Fast Boot is disabled in Control Center > Power settings
Try installing Zorin OS without setting up net connection. Once it is installed, you can connect to the net and run the upgrades.
In LiveUSB, you might try opening a terminal and running sudo apt install --reinstall ubiquity ubiquity-frontend-gtk (Net Connection Needed for this). Ubiquity is the Installer Program Zorin OS uses.
If your computer has a Nvidia card, try booting as nomodeset. You can do this from the Boot Grub Menu - press the e key or the tab key to enter the editor. Look for "quiet splash" and change just that portion to "quiet splash nomodeset", then exit and proceed to boot, then run the installer.
I had this issue too at first. I started running Zorin from USB, then I had this issue. So I hard reset my laptop and went on "Installing Zorin" instead of trying it out and the issue never came back.