If you need to verify all Windows services for Exchange are running (ie after rebooting or patching), there is a built-in Exchange Management Shell cmdlet to quickly identify if all services are running and display the ones that aren't entitled Test-ServiceHealth.  Example from Exchange 2013:

[PS] C:\scripts>Test-ServiceHealth

Role                    : Mailbox Server Role
RequiredServicesRunning : True
ServicesRunning         : {IISAdmin, MSExchangeADTopology, MSExchangeDelivery, MSExchangeIS, MSExchangeMailboxAssistants, MSExchangeRepl,MSExchangeRPC, MSExchangeServiceHost, MSExchangeSubmission, MSExchangeThrottling, MSExchangeTransportLogSearch, W3Svc,WinRM}
ServicesNotRunning      : {}

Role                    : Client Access Server Role
RequiredServicesRunning : True
ServicesRunning         : {IISAdmin, MSExchangeADTopology, MSExchangeMailboxReplication, MSExchangePOP3, MSExchangeRPC, MSExchangeServiceHost,W3Svc, WinRM}
ServicesNotRunning      : {}

Role                    : Unified Messaging Server Role
RequiredServicesRunning : True
ServicesRunning         : {IISAdmin, MSExchangeADTopology, MSExchangeServiceHost, MSExchangeUM, W3Svc, WinRM}
ServicesNotRunning      : {}

Role                    : Hub Transport Server Role
RequiredServicesRunning : True
ServicesRunning         : {IISAdmin, MSExchangeADTopology, MSExchangeEdgeSync, MSExchangeServiceHost, MSExchangeTransport,MSExchangeTransportLogSearch, W3Svc, WinRM}
ServicesNotRunning      : {}

This cmdlet is great to identify which (if any) services aren't running, but you're still forced to manually start any stopped services.  A script is saved here written to run the Test-ServiceHealth cmdlet and start any services it reports as not running.  To run the script, follow these instructions:

  1. Save the .txt file as .ps1 and transfer to the Exchange server you're working on
  2. Run Exchange Management Shell as administrator and change directory to the location of the Check-ExchangeServices.ps1 file
    1. Example - if you saved the Check-ExchangeServices.ps1 under c:\scripts, then you would need to run this command to change directory to that location:
      1. cd c:\scripts
  3. Run the script by prepending .\ to the file name and press Enter
    1. Example - .\Check-ExchangeServices.ps1