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Welcome to the forum.
Can you give us the full details of the files from the EasyCap Video Grabber? I looked at the details, but saw nothing about the files generated. The CODEC of those files will be very useful. See this FAQ Entry: http://forums.adobe.com/thread/440037?tstart=0
That will very likely tell the tale.
All versions of Premiere (Pro and Elements) only work with Firewire capture devices... not USB
If the files created by that device are compatible you may edit in Premiere Elements... after using other software for the capture process