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comment Mysql database didn't connect through sqlyog or any other mysql software?
The number in parentheses at the end of the error (not included in your question) is critical for understanding the specific reason why you can't connect. It may not be "permission" related.
comment mysql restoration process takes longer time
The problem with backing up the datadir is that unless mysqld is stopped when you do so, the best outcome you can hope for is that the server where you restore to will attempt to recover from the crash it will believe occurred previously, because of the inevitable inconsistencies. If the new server version is the same or newer, and the my.cnf is identical in a few important ways, then yes, this works. We use a simiar process, when possible, for cloning replication slaves.
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