I just dowloaded the trial of elements 11 two days ago, but it says that trial has expired.

pse may have detected a previous installation or maybe it just screwed up.

in either case, there's nothing easy you can do to restart the trial on that computer.

you can reformat your harddisk, use a new os harddisk or use a new computer to restart the trial.

I don't think there is much you can do about it, but here's a help document that might explain why it happened.

Trial mode expires prematurely
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http://helpx.adobe.com/x-productkb/global/trial-software-expired-early.html