Start an Impress video in the middle? [closed]

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I don't know of any way to achieve this in Impress currently (LibreOffice 3.5.2).

You can use some video editing program to crop the file before inserting it in presentation. Open-source cross-platform applications include Avidemux, Blender, Jahshaka. There are number of others, for example VirtualDub for Windows, which should run on other platforms using Wine.

You might also consider filing a feature request in LibreOffice Bugzilla, although something connected with this question but more broader in scope was already proposed as one of Development Ideas.