SharePoint 2010: Profile Synchronization Service will not start - no logging

The server names were changed (in the configuration database) to be something other than the NetBIOS machine name.  For example, the machine names may have been changed to be the fully qualified domain names, or the IP addresses. 
When the ProfileSynchronizationSetupJob timer job runs, it checks to see if the server name as stored in the configuration database matches the server name in the system environment variable.  If they don’t match, it silently exists and logs nothing.

You can check for this condition by running this PowerShell on the server that you are trying to start the Sync service on:

Write-host "SharePoint Machine Names:"
$farm = get-spfarm
$farm.servers
# This will list the server names (as SharePoint sees them) for every server in the farm.

write-host " "
write-host "--------------------------------------------------"
write-host "System Machine Name:"
[system.environment]::machinename
# This will list the server name stored in the environment variable.

-- If the names don’t match, for example if the system variable is the short Netbios name, and the name stored in SharePoint is the FQDN, you have this problem.

Example Output:
SharePoint Machine Names:

Address            
-------            
WFE1
App1.Contoso.com
SQLServer
 
--------------------------------------------------
System Machine Name:
App1

-- We have this problem with the App1 server.  "App1" is not equal to "App1.Contoso.com"