Further to Wytwun's link you can check the grub setting fairly quickly from the grub prompt.
Provided you have the grub> prompt (not grub rescue>) it implies grub is running but the necessary files aren't where grub thinks they should be. This might be fixable but because your installation didn't complete the state is unknown and re-installation might be the better option.
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Look for the line beginning 'root=', it should look something like
This is where grub is trying to boot from, make a note of it.
Begin checking what is actually on the disk by listing the partitions on the system
The partition names should look something like
(hd0,msdos1) or (hd0,gpt1). The numbers may be different on your system.
Now check each partition for a 'root/' directory.
Repeat the 'ls' command followed by a space, then each partition in turn and finally slash '/'.
Regardless of the 'msdos' or 'gpt', you only need the partition number.
The commands will look something like this, but replace the hd and partition numbers to suit your system.
For any partition with a root/ directory you can investigate what may be on it.
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Code:
cat (hd0,1)/etc/llver
again, you must replace the disk and partition numbers with your system. The 'llver' file (if found) should have a valid LL release number. As you've tried to install 6.2, the contents of this file should be 'Linux Lite 6.2'
If you can't find the llver file showing 'Linux Lite 6.2' in any partition you need to re-install.
If the root partition line from the 'set' command is the same as the partition in which you found 'Linux Lite 6.2' then grub is set correctly and you probably need to re-install.
If the root partition line from the 'set' command is not the same as the partition in which you found 'Linux Lite 6.2' then grub can be changed from the grub command line. However it may still not boot properly due to the failed install.
Let us know what you find and also what problems you had that lead you to the conclusion that system won't re-install.