Symptom: When trying to start the SQL Server service, it fails and says to check the System Event log. Event Viewer shows the following:

The SQL Server (WASPDBEXPRESS) service terminated with the following service-specific error:
The client and server cannot communicate, because they do not possess a common algorithm.

Cause: In most cases, this is caused by IIS running on the same server as SQL Server with the SSL 3.0 and/or TLS 1.0 disabled.
Resolution: If possible, Microsoft recommends running IIS and SQL Server on separate server machines. Where that is not possible or practical, you will need to enable SSL 3.0 and/or TLS 1.0 in the IIS configuration.

If you are not running IIS on the same machine but are still getting this message, you can enable SSL/TLS in the registry. In regedit, navigate to HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols. In Protocols, if you have folders for SSL 3.0 or TLS 1.0, open them and look for either Server or Client. Within the Server and Client folders, if there already exists a DWORD entry for Enabled, Modify that entry and set it to 1. If there is no Enabled entry, create one by right clicking and select New > DWORD (32-bit) Value, name it Enabled, then set it to 1.