The laptop has Z17, but doesn't boot. It shows 'Exiting PXE-ROM', then goes to boot options :(

Most likely, yes.

The fact that it doesn't boot from the hard drive means that it cannot find a suitable OS to boot into, which is why is skipping into the next options which would typically be external media devices (USB, other external hard drives, etc), CD-ROM and PXE-ROM (Network boot).

Sounds like you will have to re-install, and for lack of a better option (USB) you'll have to do so from another computer connected to the same local network. Wi-Fi doesn't typically work during the early stages of the boot process so you'll have to make sure you connect this laptop to the home router using an ethernet cable. Next, you need to setup an TFTP/PXE server on another computer on the network which should also have the ZorinOS ISO. You can take a look at this thread for more details on how to go about doing that.

Instructions are for Linux but this should at least give you an idea on how the overall setup works so you can research similar steps for Windows.
Alternatively, you can install Linux on a virtual machine within your Windows computer and follow the guide from there. As long as the virtual machine is able to communicate to the local network it should work all the same.
Another alternative is to live boot Linux in your Windows machine. Live Boot means that nothing is written to disk so your underlying Windows installation is left untouched, while still being able to run Linux on top of it.
Or create a small partition on the hard drive for a proper Linux installation on follow the guide from there.

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