... if you click ctrl+alt+del is there a processes named eicar.com running?
I don't think that it will appear in the task manager as eicar is not resident or long-running process.
I think it will be better to start 'command' or 'cmd' window and run the eicar.com executable from there. Then you can see if eicar.com program printed out its 'EICAR-STANDARD-ANTIVIRUS-TEST-FILE' test string or not.