I wonder if you need the HWE?
sudo apt install linux-headers-generic-hwe-20.04 linux-image-generic-hwe-20.04 linux-modules-extra-5.11.0-37-generic
It says it's already the newest version.
That means you already have the latest kernel installed.
Type uname -a
Post results here...
Is that even possible in Zorin OS 16 ? Because i never got that option.
Yes, it shows as Zorin Desktop on Wayland.
When i used zorin i had not that option at login screen. Weird.
Linux james-HP-EliteBook-750-G1 5.11.0-37-generic #41~20.04.2-Ubuntu SMP Fri Sep 24 09:06:38 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux
Does this look correct?
From a kernel standpoint, this looks very correct! @Aravisian What do you think? This look correct to you? It does to me. 
Yes, that is the current latest Kernel on Zorin OS. But clearly, something is not working right. It is possible that the 5.11 kernel has some Intel regression.
I wonder if the 5.8 kernel might work.
If you want, you can test it:
sudo apt install linux-headers-5.8.0-63-generic linux-modules-5.8.0-63 linux-modules-extra-5.4.0-63-generic linux-image-5.8.0-63
Once installed, reboot, then tap the esc key repeatedly beginning at the Motherboard Splash Screen to pull up the Grub Menu with Recovery- Advanced Options for Zorin > Then arrow key down to the 5.8.0-63 kernel and select that to boot up from.
Ok. Before I waste too much of your time, do you think it's a software issue? If it's hardware I can buy the screen and try it.
I wanted to get screenshots of the display settings and it offered 40hz as an option. Today is the first time I've seen that.
Also, while typing this up, it did the weird resolution thing. I swapped it to one of the other 1360x768 options and it came back on fine.
I appreciate the help. It's a very annoying problem to be having on such a nice laptop. It makes me hesitant to use it for online classes as you need to exit out of the desktop to clear it up.
Thanks again.
James
Also, I got this...
Reading package lists... Done
Building dependency tree
Reading state information... Done
E: Unable to locate package linux-modules-5.8.0-63
E: Couldn't find any package by glob 'linux-modules-5.8.0-63'
E: Unable to locate package linux-modules-extra-5.4.0-63-generic
E: Couldn't find any package by glob 'linux-modules-extra-5.4.0-63-generic'
E: Unable to locate package linux-image-5.8.0-63
E: Couldn't find any package by glob 'linux-image-5.8.0-63'
I have no idea.
But I prefer to exhaust software possibilities as much as we can, since those solutions do not require rushing out and buying something which may or may not work.
I am a mechanic by trade- so yuo can imagine, I have a very low opinion of the "Throw new parts at a problem until the problem goes away" approach.
Proper Diagnostics are the Proper approach.
Sadly, I am better with cars, then I am computers.
Incidentally... Have you upgraded since installing Zorin OS? Just... in case...
sudo apt update && sudo apt full-upgrade
That is very odd. 
I checked the packages in my terminal prior to submitting that post.
Can you open Software & Updates from the app menu and under the section Download from - Check if you are on Main Server.
It was set to "Main Server for United States." I changed it to Main Server.
It is downloading 13 updates from the sudo apt command now.
What kind of cars do you work on?
Classic car mechanic and Restoration. I do, however, begrudgingly work on the New Junk in between 
I enjoy the many months that can stretch where we are too busy to take in anything newer than 1970's vehicles.
Since Covid... It has been... interesting...
That sounds like the ideal way to be a mechanic. I did a short stint at the local Ford dealership and loved it. They got bought out and it turned into a "squeeze the last cent out of everyone you can" thing.
My dad and I both enjoy cars. He's a little more old school hot rodding and I'm a cool old car but focus on racing guy. I'm building an 89 Mustang, he's building a 94 Mustang and my brother just picked up a turbo 92 Mustang.
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This is a welcome response. the usual reaction I get is the "Oh you're JUST a mechanic."
A lot of people seem to think we don't need to know math to do mechanical. I use calculus more often than trig.
In the shop, when someone comes in with that attitude, I like to point at something like a Dana 7:62 and ask them to toss me the appropriate speed gear. And when they look confused, I say, "Clock is ticking."
Processing triggers for libc-bin (2.31-0ubuntu9.2) ...
libdvd-pkg: Checking orig.tar integrity...
/usr/src/libdvd-pkg/libdvdcss_1.4.2.orig.tar.bz2: OK
libdvd-pkg: apt-get check failed, you may have broken packages. Aborting...
I'm not sure if this is important or not?
sudo apt --fix-broken install
The mechanic pay scale needs to be adjusted to the times. Factor in the complexity of keeping them reliable, dealing with government regulations, and the fact that the majority of people can no longer change a tire should be making it a much more valuable profession. Not to confuse that with the increase in shop rates over the last few years that really didn't do much to increase actual pay.
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Reading package lists... Done
Building dependency tree
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.