Restoring from Time Machine

then look at the other side of the -OR-

Your Apple-ID got clobbered when your MacOS was damaged, and the Mac App store does not recognize your Apple-ID any more.

Try launching Recovery with Shift-Option-Command-R and see if it will give you a really old version of MacOS (shipped in the box equivalent) and then upgrade from there.

More options might be available using a USB-stick installer version if you have another Mac that could run an overlapping version of MacOS.

<<. "cannot make contact with the server". >>

There are two main reasons why a Mac can not make contact with the server that provides macOS:

• Date&Time are not correct within five minutes, so you cannot make a secure connection

• The Apple-Id currently associated with the computer (required to obtain any UPGRADED versions) is not a valid Apple-ID, or no Apple-ID was included in the request (because it was unknown or damaged).

do you have reason to believe that date&time are damaged or inaccurate?

have you been able to make regular internet connections when your macOS was working?

TIME:

Before 10.14 Mojave: 

sudo ntpdate -vu time.apple.com

10.14 and later:

sudo sntp -sS time.apple.com

If you have a web browser available you can also use: http://time.is 

Try reinstalling the OS through recovery mode:

How to reinstall macOS - Apple Support

have you repaired the disk with Disk Utility?

Then my recommendation is to restore your MacOS using Recovery.

You should be offered your currently-running system, High Sierra. (except my notes suggest the current version is 10.13.6.)

<<. it doesn't work >>

could you be much more specific, please?

what exactly does not work?

at what point does it fail?

what error messages do you get?