Recover MySQL ibdata1 file
What You make right - it is backup all files from /var/lib/mysql

all other steps - wrong

Your current error (in PHPMyAdmin with phantom tables) - because You have Your database folder with .frm files for table structure, and empty (new) ibdata.

What You can do now - revert all back (restore files in it original place)
Then You can:
- check error log file, for error message
- start change innodb_force_recovery from 1 to 6