Problem seems to have resolved itself. Logged back into my blog as admin after 24 hours and was able to download and install Jetpack automatically.
Can’t explain it, but there it is.
The automatic update from the Dashboard failed repeatedly, so I tried a manual update of 3.8 using FTP and cpanel from the BlueHost site, which appears to be successful. However, the updates/re-installs of the plug-ins from the dashboard seem to have the same problem. I have not tried manual updates of the plugins, because I would prefer to have everything working via the dashboard, and not have to manually update everything in the future via FTP and the BlueHost back-end, which is very cumbersome.