Problem description

If I leave my PC off for a few days and then power up, it will go into a continuous re-boot loop UNLESS I disconnect the video cable (HDMI, DVI-D or VGA) let the PC fully boot and then plug the video cable back in.

The boot process usually gets no further than the Asus splash screen but sometimes it gets as far as the OS login screen, then it starts to re-boot. I've tried Windows 10 and various versions of Linux ALL with the same result. Once it has booted successfully, it will continue to do so unless powered down for a day or two in which case the problem re-appears. It happens no matter which video port I use - HDMI, DVD-I or VGA.

Now here's the weird thing.

Exactly the same problem
was happening with a previous Gigabyte mobo. I did ALL possible substitutions including the PSU and cables until there was nothing left to substitute. I then did a complete tear down and rebuilt the system from scratch, carefully re-seating the CPU, making sure the RAM contacts were clean, etc, etc. NOTHING worked. Every few days the problem came back. In the end I accidentally damaged the Gigabayte mobo through clumsiness so I binned it.

I then purchased this brand new Asus motherboard, CPU, RAM and even a new monitor. Just when I thought all was OK, back the problem comes again! It's a whole new system!! The only carry over from the old system is the PSU and cables all of which have been substituted again just in case. Same result. I thought I was getting somewhere when I stumbled on the trick of disconnecting the video cable but how do I explain 3 three different video ports and two different monitors? I'm now beginning to suspect witchcraft!

I know this is a really long shot but if anyone can suggest anything or any test I haven't tried to help pin this down, I'd be very grateful.

System spec.
Motherboard: Asus-Prime B360M-A
BIOS: 0403 x 64 (04/18/2018)
CPU: Intel Core i3-8100 3.6GHz
RAM: Corsair Vengeance DDR4 2 x 8GB 3000MHz
Monitor: Philips 226E7 21.5in
OS: Windows 10, Linux Fedora Workstation 29