I have the exact same problem. I started having the problem with MS Office 2008 after I installed a new harddrive in my imac (24-inch, Early 2009), OS X 10.8.4. Everything was working fine and then when I try to open any Office app, the icon bounces in the dock, and nothing happens.
I as searched for solutions, the obvious fix was to uninstall office (even all of the excess system files it leaves even after an uninstall). When I a re-install Office 2008, it works for about 1 week and then it stops working again.
Next I thought to try the new version of Office (Office 2011), so I did the trial download, and sure enough got the same problem. After about 2 weeks, it stopped responding. I have talked to MS support about this problem, and their suggestion was to uninstall and then reinstall, which I am becoming an expert at.
I am also having an issue with Apple Mail and contacts becoming disconnected. When created a new mail, typing in the receiptant does not pull up their email address even though it is in my address book. The fix for this, which I do even other day is to delete a system folder in Library/Containers/com.apple.mail. I do that, and it works for a few days.
Any suggestions would be great.