MySQL service stops after trying to grant privileges to a user
I think your problem boils down to a misalignment of grants.

When you run this query

SELECT COUNT(1) column_count FROM information_schema.columns
WHERE table_schema='mysql' AND table_name='user';


You should the following number


If you get 43, MySQL 5.6
If you get 42, MySQL 5.5
If you get 39, MySQL 5.1
If you get 37, MySQL 5.0


It simply means you forgot one more upgrade step

# mysql_upgrade --upgrade-system-tables


This should fill in the missing columns.

I discussed this before


May 01, 2013 : Can I find out what version of MySQL from the data files?
Apr 24, 2014 : mysql: Restore All privileges to admin user (StackOverflow)


Since you said that mysql.user has 39, than means you did not run mysql_upgrade --upgrade-system-tables when you went from MySQL 5.1 to MySQL 5.5.

To be honest with you, I do not know if running mysql_upgrade --upgrade-system-tables in MySQL 5.6 will successfully realign mysql.user two versions back.

I would suggest making a copy by doing the following

net stop mysql
cd D:\MySQL\mysql
copy user.frm user1.frm
copy user.MYD user1.MYD
copy user.MYI user1.MYI
net start mysql


After making the copy, go ahead and run mysql_upgrade --upgrade-system-tables. Login to mysql and run SELECT COUNT(1) column_count FROM information_schema.columns WHERE table_schema='mysql' AND table_name='user'; again. Hopefully it will read 43.

If it does not, copy the user files back like this

net stop mysql
cd D:\MySQL\mysql
del user.*
move user1.frm user.frm
move user1.MYD user.MYD
move user1.MYI user.MYI
net start mysql


If you want to change the design manually, try the following:

Create mysql.user_new with MySQL 5.6 layout

CREATE TABLE mysql.user_new (
  `Host` char(60) COLLATE utf8_bin NOT NULL DEFAULT '',
  `User` char(16) COLLATE utf8_bin NOT NULL DEFAULT '',
  `Password` char(41) CHARACTER SET latin1 COLLATE latin1_bin NOT NULL DEFAULT '',
  `Select_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Insert_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Update_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Delete_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Drop_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Reload_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Shutdown_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Process_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `File_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Grant_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `References_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Index_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Alter_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Show_db_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Super_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_tmp_table_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Lock_tables_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Execute_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Repl_slave_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Repl_client_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_view_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Show_view_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_routine_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Alter_routine_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_user_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Event_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Trigger_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `Create_tablespace_priv` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  `ssl_type` enum('','ANY','X509','SPECIFIED') CHARACTER SET utf8 NOT NULL DEFAULT '',
  `ssl_cipher` blob NOT NULL,
  `x509_issuer` blob NOT NULL,
  `x509_subject` blob NOT NULL,
  `max_questions` int(11) unsigned NOT NULL DEFAULT '0',
  `max_updates` int(11) unsigned NOT NULL DEFAULT '0',
  `max_connections` int(11) unsigned NOT NULL DEFAULT '0',
  `max_user_connections` int(11) unsigned NOT NULL DEFAULT '0',
  `plugin` char(64) COLLATE utf8_bin DEFAULT '',
  `authentication_string` text COLLATE utf8_bin,
  `password_expired` enum('N','Y') CHARACTER SET utf8 NOT NULL DEFAULT 'N',
  PRIMARY KEY (`Host`,`User`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 COLLATE=utf8_bin COMMENT='Users and global privileges';


Move the Grants from Old to New

INSERT INTO mysql.user_new
(Host,User,Password,Select_priv,Insert_priv,Update_priv,Delete_priv,
Create_priv,Drop_priv,Reload_priv,Shutdown_priv,Process_priv,File_priv,
Grant_priv,References_priv,Index_priv,Alter_priv,Show_db_priv,Super_priv,
Create_tmp_table_priv,Lock_tables_priv,Execute_priv,Repl_slave_priv,
Repl_client_priv,Create_view_priv,Show_view_priv,Create_routine_priv,
Alter_routine_priv,Create_user_priv,Event_priv,Trigger_priv,ssl_type,
ssl_cipher,x509_issuer,x509_subject,max_questions,
max_updates,max_connections,max_user_connections)
SELECT
Host,User,Password,Select_priv,Insert_priv,Update_priv,Delete_priv,
Create_priv,Drop_priv,Reload_priv,Shutdown_priv,Process_priv,File_priv,
Grant_priv,References_priv,Index_priv,Alter_priv,Show_db_priv,Super_priv,
Create_tmp_table_priv,Lock_tables_priv,Execute_priv,Repl_slave_priv,
Repl_client_priv,Create_view_priv,Show_view_priv,Create_routine_priv,
Alter_routine_priv,Create_user_priv,Event_priv,Trigger_priv,ssl_type,
ssl_cipher,x509_issuer,x509_subject,max_questions,
max_updates,max_connections,max_user_connections
FROM mysql.user;


Update the Create_tablespace_priv for root

UPDATE mysql.user_new SET Create_tablespace_priv='Y' WHERE user = 'root'; 


Flip the Switch

ALTER TABLE mysql.user RENAME mysql.user_old;
ALTER TABLE mysql.user_new RENAME mysql.user;
FLUSH PRIVILEGES;


Give it a Try and See if everything works !!!