I don't know what the problem would be. Based on the efibootmgr output you posted in post 4 Ubuntu is 0000, so the command I suggested in my post above (#9) would have set 0000 ubuntu to first boot. In the command below, that is a lower case letter O for order, is that what you used? The update-grub will only work from the booted and installed Ubuntu. You could also chroot as suggested above and what you need to access is the Ubuntu partition on sda6. Doing a chroot to re-install Grub is explained at the Ubuntu documentation site below, a little over half way down the page. Read it carefully and skip the steps discussing RAID and LVM as you don't use them. Just above the chroot explanation is an explanation of using a Live CD to re-install Grub. You can try either or both if one fails.

https://help.ubuntu.com/community/Grub2/Installing

When you boot the computer and hit whatever key it shows to access boot options, do you have an option to "Boot from EFI file". I have that on my laptop but don't know that it is available on all systems but if you do have something similar, you should be able to select ubuntu there.

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i'm a newbie at grub2 and think some want to keep newbies "using distro disks" (not make it easy)

my first guess is grub.cfg is "wrong" for your default boot choice.

try:

grub-mkconfig --help

try:

editing /boot/grub/grub.cfg

however: grub2 can apparently be installed to have a built-in cfg (not be in /boot/grub/grub.cfg), i say that to warn you if you correct grub.cfg you *might* still get the built-in cf. i dunno.

If you look at the boot repair output in the link from post #4, the grub.cfg file has correct entries for Ubuntu, windows and Mint (at least the sda4 partition). The sda4 Mint grub.cfg has the correct entries also. The problem with an EFI install with Mint and Ubuntu is that Mint creates an 'ubuntu' directory in the EFI partition and puts its files there.

If the OP ran the efibootmgr command to set the order to the Ubuntu entry, it should have changed and he should have been able to boot. Problem is, because Mint uses ubuntu in EFI and the OP has two different installs of Mint, there is no telling which one of the 3 he has there.

If the op boots into the linux installation that the op uses for their main installation and run should work.

The problem is though, from his most recent post, that he can only boot windows for whatever reason. Not sure exactly what he did so no way to know.

TSorry about that, I was going by the op first post, missed that the op can now only boot into windows.
From the live usb connected to the internet open a terminal:
Code:

I don't think re-installing Grub is going to help. He already has Grub installed with a good grub.cfg file on sda6(Ubuntu) so setting the ubuntu to first priority on the EFI menu using efibootmgr should do that since he also has the Ubuntu efi files on the efi partitions.

Something went wrong when efibootmgr was used, This doesn't redo the grub.cfg file, it should reinstalls the grubx64.efi to the efi partition and makes it the first boot entry

yancek and colorpurple21859, you have both been very diligent and helpful. My system is really messed up, as yancek has already noted.

I think my system is so balled up that it is just too complex to try to get it solved in its current state. Sometimes it's best to go with the simplest approach, which is installing Windows 10, and then installing Ubuntu, as Keruskerfuerst has already suggested.

At least I have learned more about efi and boot manager, so thanks to everyone for your posts.

I'll install Windows 10, even though it is already installed. Then, I'll install Ubuntu. Then I'll let it rest. I'll post back here with results. Thanks again, all.

Oh, I did execute the commands that colorpurple21859 suggested in the 6:00 PM post from today. I rebooted, no difference, it went right into Windows again. Just thought I'd give feedback on your post, colorpurple21859. Thanks for that.

yancek, in an earlier post you suggested that there may be some key to hit to bring up the boot option screen. Well, having nothing to lose, I hit the "del" (Delete) key as the computer booted, and Voila! The boot screen came up!

I thought I was all the way there, however, it didn't recognize my password as I was booting into Ubuntu. So I rebooted again, and selected Ubuntu, and this time it did recognize the password, and I successfully booted into Ubuntu. That surprised me. I didn't know it, but it looks like computers are a little like engines, in that they have to be "warmed up" in order to start successfully.

It was crucial that I was able to boot into Ubuntu, as I had to backup files first before installing Windows again. I have now backed up all my files.

Now, I don't even have to hit the "del" key, the boot option screen comes up automatically. And by the way, I can indeed select Ubuntu, Windows, and even Linux Mint.

So since the problem has really been solved, I think I will just leave things the way they are. My thanks go out to all of you who responded to this thread, especially yancek. You have all shed some light on my problem and helped me through this. I know my system is still a mess, but at least it works!

Great to hear, coderlen.

If you want to, you can mark the thread as "Solved" - see "Thread Tools" at the top of the thread.

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hydrurga, thanks for your post! I was just searching for a way to close the thread. Thanks so much.

No problem. It was good of you to come back on to the thread and let us know what had happened. If you still feel that there are aspects of your system that are a "mess" then please do come back on and create a thread to get these sorted out.