Thanks to a partial solution here, the problem was fixed by deleting the
*.tmp files in the following two directories:
C:\Documents and Settings\myusername\Local Settings\Application Data\Google\Chrome\User Data\Default
C:\Documents and Settings\myusername\Local Settings\Application Data\Google\Chrome\User Data
Or for Windows 7:
There were 65,535
*.tmp files in each! They had names like
1.tmp through to
FFFF.tmp. All of these files were empty. It took quite a bit of time to even list the files in each directory, and Windows Explorer stalled while trying to operate on them, so I used bash to delete them. It seems that the reason for the slow-downs and the incorrect shutdowns of Chrome was that it was trying to access the files in some way. Maybe it was only trying to list the files in the directory, which by itself would take a long time.
Now Chrome starts up instantly, and shuts down almost instantly, and does not display the message.