Symptom

When you try to start the SQL Server service, you get a message:

Windows could not start the SQL Server (WASPDBEXPRESS) on Local Computer. For more information, review the System Event Log. If this is a non-Microsoft service, contact the service vendor, and refer to service-specific error code -2146893007.

Cause

SSL 3.0 and/or TLS 1.0 have been disabled.

Resolution

Reenable these protocols, by adding or altering registry key values.  For each of the following keys:
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.0\Server
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.0\Client
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\SSL 3.0\Server
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\SSL 3.0\Client
Create new or edit the existing value: Name: Enabled, type: REG_DWORD, value: 1

The SQL service should now start without error. If the change has not taken effect, reboot the PC.

Additional Information

If there is any DisabledByDefault key value present, it may be necessary to delete it or change its value to 1. (Mark down the value and path before doing so.) Windows Server OS may need to be rebooted after changing this.

Discussion:
https://dba.stackexchange.com/questions/82207/sql-server-service-wont-start-after-disabling-tls-1-0-and-ssl-3-0-on-windows

https://social.msdn.microsoft.com/Forums/sqlserver/en-US/5f543d1f-9483-49bb-9c65-999f287eaefa/sql-server-service-wont-start-after-disabling-tls-10-and-ssl-30-on-windows?forum=sqlsecurity

Microsoft Technet instructions to enable/disable:
https://technet.microsoft.com/en-us/library/dn786418%28v=ws.11%29.aspx#BKMK_SchannelTR_TLS10

Microsoft info about Transport Layer Security:

https://docs.microsoft.com/en-us/windows-server/security/tls/tls-registry-settings