So I understand you had Chromium on 13.10 and it got upgraded to 14.04 with all the other packages, am I correct ?
I had to reinstall it, the panel icon was not even working. I did not loose my profile settings.
I do not recall how I got it reinstalled, but that probably was with apt-get as I rarely use the GUI for package managers, I like when it talks to me in the terminal.
I would run:
and see if it helps getting Chromium back on tracks.
sudo apt-get update
sudo apt-get remove chromium-browser
sudo apt-get install chromium-browser
One thing, you did restart Chromium after installing the pepperflash plugin, right ?