Moved MySQL datadir Now Server Will Not Run!
I have done the same thing. Be absolutely sure that all rights and owners are intact. You can do this with cp -rp if I'm correct. Rsync the folder locally should also keep owners and rights intact. You don't have to change the config however. A symlink will do. 


Rename the original datadir to datadir-old or something similar. 
Then create a symlink to the new location. 
If you want the symlink to have right owner, create a new folder (tmp), move the symlink inside that folder, then change the owner of the tmp folder and its contents, then move the symlink back.
Undo the changes to the config files. 


On the commandline... (I haven't tried this so check if all is as it should be!)

sudo -i
cd /var/lib
mv mysql mysql-old
ln -s /home/mysql mysql
mkdir tempdir
mv mysql tempdir
chown -R mysql:mysql tempdir
mv tempdir/mysql .
rm -rf tempdir


In the directory listing I see the following on my system. Yours should be similar!

drwx------  7 mysql         mysql          4096 Feb  6 12:01 mysql  



-rw-rw----  1 mysql mysql 1671430144 Feb  6 17:37 ibdata1  
-rw-rw----  1 mysql mysql    5242880 Feb  6 17:37 ib_logfile0  
-rw-rw----  1 mysql mysql    5242880 Jan 28 14:35 ib_logfile1  
drwx------  2 mysql mysql      24576 Jan 28 14:34 testdatabase_local  
drwx------  2 mysql mysql       4096 Jan 28 13:38 mysql
-rw-rw----  1 mysql mysql          6 Jan 28 13:38 mysql_upgrade_info
drwx------  2 mysql mysql       4096 Jan 28 13:38 performance_schema


Try this and see if that fixes your problem.