Go back into Services, check and enable Event Log Service.
Startup Type should be set to Automatic.
If the Event Log service is missing, there is probably a problem with your registry.
Check this location in your registry:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\
Services\Eventlog
If it is missing, export the key from a working system and import it in to your system.
Remember to backup your existing registry before completing the above task!
Please note: Playing with the Registry can be disastrous if you do not know what you are doing. I would recommend asking an IT Person to help. I do not offer any guarantees and cannot be held responsible if anything goes wrong.