Remove expired certificate SQL Server
Sounds like you may have deleted the certificate from the certificate store prior to unbinding it from SQL Server.  I haven't tested it yet, but I'm guessing that if you did that, no certificate would be shown in the SSCM dialog because it would be trying to find the certificate that matches the thumbprint stored in the registry, but wouldn't be able to find it.

You may be able to fix this by clicking on the "Clear" button in SSCM where the certificate is configured.  IF this will clear the thumbprint that is stored in the registry, then SQL Server will start, but it's possible that the "Clear" button won't work if it can't find the certificate.

If that doesn't work, check the Certificate value in the registry at: 

HKLM\SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL.12.MSSQLSERVER\MSSQLSERVER\SuperSocketNetLib


The registry path will be different if you're using a named instance.

If it's not blank, then SQL Server will try to find the certificate that matches the thumbprint that is stored there.  If it doesn't find the certificate, then it fails to start.  If the certificate has been deleted and the Certificate value in the registry still contains a thumbprint, then just save what's there and then delete the thumbprint so that it's blank.  Once that is done, SQL Server should start.

Lastly, if you already have the new certificate, you should be able to install it in the certificate store, bind the service to it in SSCM, and SQL Server should start.