When this problem first occurred I checked all my hardware, everything was 100%. But it certainly is starting to look like a compatibility problem with the onboard Intel graphics.

Yeah, I do lean more towards hardware. Reason I mention monitor settings is because every monitor has a default refresh rate which is it's optimum refresh rate, many folks do change it to a higher value if this setting is available, which is not the monitor's optimal refresh rate. For the sake of troubleshooting, it's a good idea to try setting the monitor to default settings.

But... what unique configuration features do these distros have/use that allow them to work properly, do they detect default settings in some hardware component and apply those settings? Or do they compensate for something apparently out of whack?
EEIT: Cables and connections: good to try a different set of cables, and have a look inside the connections, there could be a sunken sheath in the female end, or a bent/sunken pin in the male end, or just dirty, corrosion.

I just updated the BIOS on my GA-H97M-D3H, OpenSUSE is no longer different than any other Distro.

There are now 3 different results when I boot Windows from GRUB:

70% of the time I get a BSoD with varied error messages.

30% of the time I get either a corrupted GRUB splash screen or a normal window shifted up so the top half is a normal Windows screen and the bottom half is a corrupted GRUB splash screen.

10% of the time Windows boots normally.

I can't determine any pattern, the results just seem random for any Distro.

I borrowed a video card and installed it on the GA-H97M-D3H and everything worked as it should including booting into Windows. This was just a test and I don't plan using a video card in this machine. I tried using Boot-it but it couldn't detect some of the boot partitions, though I didn't pursue it too far. I ended up installing System Commander, it seems to work fine but I don't know if its a good permanent solution.

I found 3 other cases like mine online, with GRUB booting Windows hiding behind a blank screen. All involved Intel Series 6 & 7 onboard graphics and were not resolved.

Just an update. To date I have no solution. There are a few workarounds.

1/ Install a video card. This worked 100%.

2/ Use BURG as a boot manager. This was the best software solution and worked much as GRUB except it booted Windows.

3/ Use System Commander as a boot manager. This worked OK but is limited to ext3 and is far from being as automated as GRUB or BURG.

I have been using BURG for 2 weeks with few problems. Of all the boot loaders I tried GRUB was the only boot loader that couldn't boot Windows.

Thanks to everyone who posted.

This is the normal? behavior when selecting Windows 7 from the GRUB menu

When the Windows partition is healthy Windows boots and runs but the display is a corrupted image of the GRUB splash screen.

When Windows is in an error state Windows boots with everything working normally.

This is a workaround I found. I boot into Linux Mint 19.1 which is controlling GRUB and edit the /boot/grub/grub.cfg changing the Windows Volume Serial Number. Then reboot and select Windows at the GRUB menu. This generates the following GRUB error

No such device: "16 digit number"
Setting partition type to 0x7

Press any key to continue

I press a key and it successfully boots Windows with video.

This of course will work until the next update-grub then I would change the Volume number again.
What different parameters does GRUB use that it boots successfully after the error screen.

When you refer to 16 digit number, do you mean the UUID for thee windows partition with the boot files? That should not change, at least between boots. Does the UUID you see in grub.cfg for windows match the UUID you get with the blkid command?

Yes,the 16 digit number refers to the number entry I made for the Windows UUID or what I called the Windows volume Serial Number in /boot/grub/grub.cfg in order to generate the GRUB error. No it does not match as I purposely made it different.

Given you have so many motherboards to choose from, you might wish to try one my way, essentially the same for two decades plus (with Win10, WinXP, Win98SE):

1-"Generic" code on MBR always
2-small primary partition for Windows bootloader (FAT or NTFS, depending on Windows version; sda1)
3-small FAT primary partition for FreeDOS (sda2)
4-400MB or less EXT2 primary partition for master (Grub) bootloader with boot flag set, never mounted as /boot, managed by myself alone (sda3)
5-lots of logical EXT3 or EXT4 / partitions for Linux installations, /home, /usr/local, plus swap and two NTFS (separate system and user data)
6-Windows gets installed after first (or more) Linux installation(s)
7-boot flag gets moved temporarily to sda1, first, when Windows updates require, or to install Windows
8-no Linux installs Grub anywhere except on its own /
9-all partitioning done by myself in advance of installing anything, using the same non-FOSS cross-platform partitioning application
10-os-prober is either disabled or not installed

On my two Win10-equipped PCs, only various openSUSE flavors have been installed. Those with 98SE or XP have Fedora and/or Debian and/or *buntu and/or Mandrake/Mandriva/Mageia and/or Mint and/or Gentoo in addition to multiple openSUSEes. Boot screens behave as expected in every case, including Plymouth either not installed or disabled.

A while ago I tested another P8B75 motherboard that is connected to my TV and it was 100% OK. This is not the same board I referred to earlier, that board was used and had other stability problems. It's also possible that board was booting to a plain blank screen. When I later noticed Windows was functioning behind the blank or corrupted screen on the other boards, I had already discarded the faulty P8B75 and never actually tested if Windows was running behind the blank screen. I had assumed it had the same characteristics as the B85 and the H97M-D3H.

The H97M-D3H that I have done 90% of my Linux testing on has another problem, it corrupts USB NTFS partitions when unmounting, not on spinners just on flash drives. I didn't notice this for some time as I normally use FAT32 and exFAT when transferring data from this computer and the few times it did happen I didn't connect it to Linux. Recently I tested several different flash drives and there is no doubt 30% of the time it corrupts the NTFS partition when unmounting.

I could easily live with the GRUB booting Windows workarounds but I don't want to risk data loss to NTFS corruption. I have decided not to use this board in my Linux computer, I'm going to switch the P8B75 and the H97M-D3H.

Saying Linux loads its drivers when booting doesn't sound very impressive until you transfer a hard drive to a different chipset motherboard and the 23 different Linux installations all work without a hitch. I am always surprised.

Unfortunately Hardware/Firmware, and Driver issues may pop up and
cause some puzzling issues in my experience. More often it is video/GPU related, at least for me.

Also I found if a new install and you want GRUB one way is to
Install Windows first, resize/adjust partitions to make room for linux and then install linux. This is because Windows will typically overwrite any other MBR bootloader during its install.

Glad you got it sorted stemwinder, Sorry for your difficulties.

All the Best,
Tim