Start User Profile Synchronization Service using PowerShell

Using Get-SPServiceInstance powershell commandlet you can get GUID details of all the Service instances running in your server. From that pick the GUID of your User Profile Synchronization service and use Start-SPServiceInstance commandlet to start the service in the server. 
 

Start-SPServiceInstance –Identity  “GUID of the Service application”

Sometimes your User Profile Synchronization service might stuck in “Starting” due to some issues in Synchronization. To Stop that service, use the below command

Stop-SPServiceInstance –Identity  “GUID of the Service application”