I wonder if there is more than one version of this story? Or more than one story with the same name? The version I'm looking at now bears some resemblance to your summary (Shakespeare is brought to the present and takes a class on himself) but does not have anything about a computer.

Edit: I've now found this story on several websites, and they are all the version I know about, with Shakespeare being brought to the future to take a class on himself, failing it, and being sent back. The end, nothing about a computer of any kind anywhere in it.