I have had a few issues with the WDS service not starting on some of my distribution points.
One server was easily fixed by checking and fixing the permissions for the SYSTEM account for the C:\ProgramData\Microsoft\Crypto\RSA\S-1-5-18 folder.
It needed to have Full Permissions to start. For some reason the permission was removed which caused the service to fail each time I started to fix it.
Another time I had this issue, it turned out to be a corrupt SQL computer account in the SCCM SQL database.
Each time I tried to start the WDS service under the System Account it would generate Failure Audit alerts in the Application Log:
Event Type: Failure Audit
Event Source: MSSQLSERVER
Event Category: (4)
Event ID: 18456
Time: 1:00:00 PM
Login failed for user ‘Domain\ComputerAccount$’. [CLIENT: x.x.x.x]
I removed the login for ComputerAccount$ from the SQL Management Studio and re-created it with the same permissions and the WDS service can now start.