It had nothing to do with anything except a security setting on my router. I had made a change on my personal network last week, and had to do a lot of resetting of devices. I didn't realize the small but pronounced effect that change would have on a couple of my devices.
I finally figured out today that it was nothing to do with Chrome or the Chromebook when I was looking at a DU post this morning with a JPEG image link that wasn't working. When I tried to open that image in another tab, it said that the the "connection has closed unexpectedly".
That wasn't the error that I was expecting, as it indicated there was something between my device and the image server causing the problem rather than my device itself. This made me think of the router change I had recently made. I just changed one security setting for the Chromebooks giving me the the problem of not being able to watch Twitter videos, bingo!: everything now works fine.
I'm no expert, but I try to fix things via trial and error. This is a classic example of thinking about any changes around the time a problem surfaces on your devices like I did to the network. In hindsight, it was IMMEDIATELY after I made the change that Twitter videos stopped working. I spent hours focusing on the device, trying to re-install the now obsolete Flash, doing resets, clearing cookies and caches, posting on DU about my device, etc. totally neglecting something outside my device like the router.
That will save me a few hours of time now that I don't have to do a PowerWash.
Thanking all of you again for your help, but this was totally a problem uniquely mine!