This command says:
That command has reset the permissions of your $HOME directory to 600. Your home directory therefore is not anymore accessible (because not executable). Try resetting the permissions to the default 755 (or alt least 700) and see if it works again.
chmod 600 $HOME/ .ssh/id_key
If it still fails, then just reinstall without reformatting your partitions. This goes quite fast, and usually repairs what is broken without loosing too much of your settings. If that still fails, then reinstall again the same way, but first move your old home out of the way (rename it). That way, a new account will be created, and there is guarantee that you will be able to log in. You can then move your data back from the old homedirectory to the new one.
Your commands as you showed them may have created more havoc. In many instances, there is a space between $HOME/ and the other elements, which causes these to be considered as multiple arguments rather than one pathname. In the example I gave, the permissions were not only applied to .ssh/id_key in your home directory but also to $HOME/ itself. Be careful with the commandline!