I have a moderately old netbook which is a dual boot Windows 7 / mint 18 boot.
Definitely a MBR boot.

I bought a 3TB usb3 external drive which arrived with two partitions one a small msft partition and the other a big NTFS partition. I reformatted the NTFS partition as ext4.

If I attempt to boot from the HDD (with the USB drive attached) it boots up.
If I attempt to boot from the HDD(without the USB drive attached) I get a GRUB menu and then it fails after a couple of minutes.
If I boot (without the USB drive attached) I get a GRUB menu and can boot into Windows.

I have created mount points & fstab uses UUID references.

I have tried a single user boot - but it doesn't accept the root password.
Interestingly, if I boot from the HDD, with the USB attached, the USB is recognised as sda whilst the HDD (the boot device) is recognised as sdb.

Live distros will boot from USB perfectly normally.

sounds like your boot order is a bit out of whack, and possibly the disk configuration of grub doesn't include your mint installation, so it may be using the USB.

One reason for the USB storage to be identified as sda is that it is initialized by the bios, then during the initial scan the disk (not yet spun up) is second.

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That's pretty close to what was going on.

Well - it's now fixed; so I shall mark this as fixed.

I thought it was a good idea to put the USB partition in my /etc/fstab file.
Well it wasn't.

I'd forgotten that USB gets automounted.
So I removed the external drive from my fstab and it was fixed.

It's a long time since I've broken Linux so unnecessary panic set in...