A Task Server is unable to register to its self because it is unable to connect to the defined web site.
The logs show the following continual pattern of failure (excerpts):
Client Task Server is successfully started, configuration: D:\Program Files\Altiris\Altiris Agent\Client Task Server\TaskServer.config
Main site of Task Server is 'SEP'.
Source: Task server ports
Can't find the task server port numbers.
Object reference not set to an instance of an object.
[System.NullReferenceException @ Altiris.TaskManagement.Common]
at Altiris.TaskManagement.Common.IISHelper.ReadPortsFromSite(String webSite)
The remote web site could not be found: 'SEP', this site will not be accessible and can lead to Task Server inability to serve remote requests.
SEP had previously been installed and was disabled or remoived, but elements of it had remained.
The string value "TsMainWebSite", under "HKLM\Software\Altiris\" was set to "SEP", so the TS service was looking for a web site named "SEP"