I am having the identical problem with Outlook and the issue it's complaining about is given away by the error message: "The database is currently stopped." Assuming this is the only problem, to start the database you need to make sure the following services are started:
MSSQL$MICROSOFTBCM
MSSQL$MICROSOFTSMLBIZ
You would of course, for best results, not be running Outlook when you started the services. Also, since Outlook maintains its own datafile (the .PST) for its own data, it's not surprising--and perhaps promising--that you would still be able to access anything stored in Outlook.
Unfortunately in my case, the problem is that regardless of the services' "automatically start" status (which you'll need to verify in yours) they fail to do so, without any indication as to why. Unlike my system, you may have events in your event log that indicate the problem--noting that error 1355 is NOT indicative if you are not on a domain.
One final item you may check is in Outlook itself. Check Help | About Microsoft Outlook | [Disabled Items]. If BCM has been disabled due to some error, it may show up in this list. It may be worth making sure you're fully patched before enabling an ailing component.
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