No matter how many times you click the Outlook icon, it never pops up on your screen. Sometimes it has started, but you would never know because the graphic user interface never appears. Try this:
1. Press the Ctrl + Alt + Del keys together.
2. Click on the "Image Name" column header (this sorts all processes alphabetically).
3. Look for "OUTLOOK.EXE".
4. Click on every instance of it and click the End Process button until none are listed.
At this point, you may be able to open Outlook.
So what happened? I often blame Outlook problems on Plug-ins. iTunes has been especially troublesome lately as the iPhone seeks to integrate with every piece of software produced thus far. The iTunes plug-in allows iPhones to synchronize with Outlook contacts. I suggest finding other ways to accomplish this, because the iTunes plug-in has been a repeat offender in cases such as this -- it will re-install itself when you update iTunes. Other repeat offenders have been Google Desktop and Skype, but these have been less common as they released updates.
How to remove plug-ins:
Go to Tools > Options > Other tab > Advanced Options button > COM Add-ins. This is where you'll find the iTunes plug-in and possibly others listed. I personally remove all of these, but by all means keep what you find valuable.
If you are still unable to open Outlook, try going to Start > Run... and type in:
(note the space before the slash)
This will open Outlook without any plug-ins. Once open, you can then disable problematic plug-ins as instructed above.
More-advanced users can remove plug-ins through the registry by cleaning out this key: