Hello! It is possible to hack some system files (ntoskrnl.exe, winload.exe and some more) and bypass the NX/PAE check so you can install Windows 8 or 8.1 32-bit in an old Pentium 4, or even a Pentium III, but the latter will be too slow to be useful. The same trick works for Windows 10 32-bit, I have tried it, but the problem in Windows 10 is that you get an error message that the digital signature or ntoskrnl.exe is invalid and have to press a key to select the Advanced Startup Options, and then 7 to disable signature enforcement (test mode). This happens AT EVERY restart! No matter what I tried, in order to load Windows 10 I had to select the Advanced Startup Options and disable signature enforcement (test mode) EVERY time. As you can imagine, it is rather annoying. But when in Windows 10, they did work without any perceivable compatibility issue.
For anyone interested, the process involves to boot with Windows 7 DVD and when at Setup screen press SHIFT+F10 to get a command prompt. Then you use diskpart to wipe the disk clean, create a primary partition and format to NTFS. Next you use the imagex.exe utility to extract the Windows 10 Setup files from install.wim to the hard disk. This is like starting the Windows Setup and getting to the point of the first restart. Before you do anything else, you use a utility to patch the relevant system files to bypass NX/PAE checks and also enable both CPU threads in hyperthreading. Having patched the system files, you restart the computer from the hard disk, NX/PAE tests are bypassed so Setup resumes and goes to the next stage. The problem is that after Setup is complete, every new restart you have to select the Advanced Startup Options and then to disable signature enforcement (test mode). So it is best avoided to install Windows 10. Windows 8 will boot to the desktop without having this issue (just enable test mode permanently) but you may need to re-patch the system files after every Windows Update, if they are replaced.
My advice: Stay with Windows 7 32-bit to avoid any issues. If you want to do it, at least install Windows 8.1 so you don't get the annoying boot sequence every time. Install Windows 10 at your own risk.
Read all the details here. You may have to register to read all content.
PS 1: Warning! If there is no WDDM driver for your graphics card (at least Vista driver), you will be stuck with Microsoft Basic Display Adapter (basic display, NO ACCELERATION). Windows 8 and 10 do not allow installing Windows XP graphics driver (XPDM). So stay with Windows 7 that will accept an XPDM driver. Windows 8 and 10 demand a WDDM driver, or you get basic graphics only. No effects, no games, not even the screensaver will work! Beware!
PS 2: Hacking the files to upgrade Windows 7 to 10 is far more complicated, almost impossible, so forget it! I did upgrade once from Windows 7 to 8 but I tried too many things to remember exactly what worked.
It is this strange behavior of Windows that can drive an average user crazy about computers... Fortunately we experts become immune after enough exposure to this madness...