Hello HomerJ,
The issue could be many different things, First I would check what the Security package actually installed or did as this could be the most evident issue related to your issue. If the security package is blocking something within the server from allowing the services to restart or to contact the DB that hosts the ALM resources. If either of these are occurring you will need to either find as way to set an exception for the service, connection, or the account to allow the services to perform as designed.

I have seen where there is a timing issue possibility if you are hosting the DB and the ALM server on the same server (this is rarely done so probably not the case here). If you have this setup then see the assistance here: http://eyeontesting.com/questions/9103/issue-with-alm-services-not-restarting-after-syste.html

Since this just happened after the above recommendations I would see that the passwords for the service account, tdadmin, and td user haven't changed or been expired/deleted. If any of these have occurred then the services will not start until the password differences are corrected in all affected places (services . account settings,. AD/LDAP system, DB instances).

These places are all the starting checks I would recommend and if all seems correct and working normally, since this is a down situation, I would recommend opening a support ticket with your ALM support group as they should be better able to assist in a timely manner on a down equipment issue.

Dan