Task Manager is usually disabled using a Group Policy, so if you're a home user and cannot run Task Manager by any means, then you may be the victim of a trojan virus. Companies may implement a domain policy that prevents execution of the Task Manager (else you could discover all of the Big Brother software they're using on you), so check with your IT department if you experience this on a work computer. One way to test this is to login to your local machine account rather than the domain and see how much access is restricted.
If Task Manager is disabled, then you will not be able to access it by any means. It will be "greyed out" on your taskbar, the option to run Task Manager will disappear when you press "Ctrl+Alt+Del", and will refuse to run by typing "taskman" in a Run dialog box.