Unfortunately, this is really not possible - at least not the way you want to do it if the university does not provide a key-based authentication API. You can always ask them nicely, but they are likely to be too busy to help. If you provide your users with full disclosure of information and ensure the security of your server, this should be enough.
In fact, there is one way to do this over the Internet without saving passwords - you can use a Java or Flash application. Unfortunately, your users need to leave the browser open while the application does its work, but in this way you will not need to store information.
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