Windows 10 won't install because it says my PC doesn't support NX ?

In addition to Windows 10's other minimum hardware requirements, there are specific requirements for the computer's CPU (processor).  In order to be able to run Windows 10 (or Windows 8/8.1), you need a processor that supports PAE, NX, and SSE2. 

No-eXecute (NX)

No-eXecute (NX) is a processor feature that allows memory pages to be marked as non-executable. The feature enables the CPU to help guard the system from attacks by malicious software. The NX feature prevents executable malicious software code from being put in accessible regions of memory. Windows 8 requires that systems have processors that support NX, and NX must be turned on for important security safeguards to function effectively and to avoid potential security vulnerabilities.

https://docs.microsoft.com/en-us/windows-hardware/manufacture/desktop/paenxsse2-support-requirement-guide-for-windows-8

However, that same article also says: "All modern processors support NX. NX can be turned off in the BIOS. Based on available telemetry data, it appears that one percent of the systems that are running Windows® 7 have NX turned off because of a misconfiguration in the BIOS setting."

So perhaps your CPU does meet the requirements but the BIOS is misconfigured.

Download and run coreinfo.exe as explained in this article:  https://www.thewindowsclub.com/your-pcs-cpu-isnt-compatible-with-windows-8/

Reminder:  you need to run coreinfo.exe from the Command Prompt. 

• Open a Command Prompt window by clicking Start, typing Command Prompt in the Search box, and pressing Enter.
• When you download coreinfo, save the downloaded file on your Desktop
• Right-click >"Extract all" on the downloaded file
• Open the folder with coreinfo.exe and coreinfo64.exe and drag and drop coreinfo.exe into the opened Command Prompt window.

The first line of the coreinfo output identifies your processor (in the screenshot in the article, it shows an AMD Athlon II x4 620).  What is the name of your processor?

What is the make and specific model of your computer?