[TheBang]

I don't think that will actually work. The activations are tied to a specific hardware configuration. So, in order to deactivate a specific computer, you have to be running the deactivation from that specific computer. Since, as joethelion mentioned, that computer no longer exists, simply running it from the old hard drive is not sufficient.

As the article you pasted says: "If your old computer is not available, contact Adobe Support."