Some screen capture apps write clips that are not exactly standard. What are the particulars of your screencapture videos? At the very least, it would be good to know the wrapper and codec. Ideally, post all the info from MediaInfo.
I'm not sure why the clips would import and behave well initially but give problems in subsequent sessions. One thing that might be worth trying: On the Media tab of the Preferences dialog, disable "Write XMP ID to files on Import." I'm not familiar with the "Enable Clip and XMP Metadata Linking" option, but couldn't hurt to try disabling that one, too.
So right now it sounds like your content is not "Media Pending" but just black. Is this true in both the Source Mon and the Program Monitor? Are all the timecodes shown in the Project panel correct--Media Start/End, Video In Point/Out Point, Audio In Point/Out Point?
When clips show as Media Pending, what Status does the Project panel show? If it's "offline," have you tried relinking (Clip>Link Media)?
How about trying with at least some of the content on the internal HDD rather than the external--just to determine whether the problem has to do with the external drive, or its cable.