Time Machine backup hangs during OS update on old MacBook Air

Hi all,

I backed up my i5 MacBook Air to an external HDD using Time Machine whilst attempting to update the OS on my machine (I know I can only update so far as it is old), but when I tried, I was told my HDD was not compatible. I then tried to change it to AFPS, but it was not available for selection on the system. I tried all the online suggestions and none worked. I wiped the HDD and then tried to just restore from my HDD backup. It goes on for ages and then hangs at the apple logo and complete white line.

I then just reinstalled Yosemite on the air, but it will not let me update the OS. I went to the apple support page on Safari and it has the "cannot establish a secure connection" so I cannot download High Sierra. I then went through every single step listed on line to resolve the Safari issue and none worked.

I have checked the MacBook drive and the external using disk utility and both are fine. I just seem to be going around in circles as the MacBook says it is restoring the files from the external HDD, but then it hangs.

I know it's an old computer, but it was doing fine. I guess I should have left it alone, but any help or advice would be hugely appreciated.

Thank you.

[Re-Titled by Moderator]

Original Title: Time Machine Hangs