Get missed transactions from slave
The thing you need to do to change, what I will call, the reference point for replication.
Since Servers B,C, and D have binlogs enabled, this will be handy.
You gave
slaveB&gt; SHOW SLAVE STATUS\G
*************************** 1. row ***************************
      Relay_Master_Log_File: master-bin.000002
        Exec_Master_Log_Pos: 1476884

slaveC&gt; SHOW SLAVE STATUS\G
*************************** 1. row ***************************
      Relay_Master_Log_File: master-bin.000002
        Exec_Master_Log_Pos: 78684

Let's sync up ServerC to be a Slave to ServerB
STEP 01 : Stop all writes to ServerC
STOP SLAVE;

STEP 02 : On ServerC, run SHOW MASTER STATUS;
Let's say the output was master-bin.000003 position 12345678
STEP 03 : On ServerC, run
mysqlbinlog master-bin.000003 &gt; latest-binlog.sql

STEP 04 : Locate position from STEP 03 and show 3 lines before and after
grep -C 3 12345678 latest-binlog.sql

Let's say the timestamp was &quot;2013-09-03 01:23:45&quot;
STEP 05 : Find the timestamp of that position in the binary logs of ServerB
Let's say the binary log on ServerB is master-bin.000004
STEP 06 : Dump position matching timestamp inside ServerB's binary log master-bin.000004
SQLFILE=dumpstuff.sql
BINLOG=&quot;master-bin.000004&quot;
DT2=&quot;2013-09-03 01:23:45&quot;
DT1=&quot;2013-09-03 01:00:00&quot;
mysqlbinlog --start-datetime=&quot;${DT1}&quot; --stop-datetime=&quot;${DT2}&quot; &gt; ${SQLFILE}

STEP 07 : Locate the timestamp inside SQLFILE and find the position
Let's say the position is 87654321
STEP 08 : Connect SlaveC to SlaveB
On SlaveC, run this
STOP SLAVE;
CHANGE MASTER TO master_log_file='master-bin.000004',master_log_pos=87654321;
START SLAVE;

That's it !!!
CAVEAT #1
Repeats all these same steps to sync ServerD to ServerB
CAVEAT #2
If you have done these steps and still don't trust the data, please download Percona Tools and use pt-table-checksum to verify each Slave against the new Master. If there are differences, you can run pt-table-sync to generate the SQL to repair the differences.
UPDATE 2013-09-05 12:28 EDT
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On Step 2,3 and 4 , I don't have access to master binlog, I guess the way to get the latest applied transaction on slaveC is to extract it (using the Relay_Master_Log_File and Exec_Master_Log_Pos from show slave status) from slaveC relay log. Am I right? Steps 5 to 8 seems to be correct.

You can use mysqlbinlog remotely using --read-from-remote-server. Besides, you do not go back to the old Master, ServerA. You are doing these things among the Slaves, making ServerB the new Master. If you are using some manged hosting company, those admins need to be involved in this process. At the very least, they could provide some SSH tunnel access to permit you to access the Linux box and all necessary folders permissions. No MySQL authentication is needed.