iTunes won't open to desktop, stays in taskbar

I haven't seen this one before.
What happens if you go into program files\iTunes and try to open iTunes by double clicking on iTunes.exe?
If it opens like that try creating a new shortcut.

Otherwise on general principles, you could try a repair install of iTunes. I am not sure how you do this in Windows 7, but I guess you will know.

This one might be a damaged iTunes display preference. (Seen similar things happen once or twice to people with the QuickTime Player, and it was a display preference issue there.)

We can check to see if a damaged display preference is afoot by checking to see if this is a systemwide or user account specific issue.

From the Start menu, choose Control Panel.
Open Add or remove user accounts
Select Create a new account and follow the instructions to complete the account setup process.
Once the new account is created, choose Log Off from the Start menu. Log into the newly created user account. (Don't use Fast User Switching to move between accounts.)

Open iTunes in the new user account. Does the setup assistant run and show you (eventually) a blank library screen? Or does iTunes stay minimised to the Task bar in the new account too?

If iTunes *does not stay minimised* in the new account, the technique you need (to check-on/fix a display preference issue) is described in the "Remove iTunes Preference files" section of the "User-specific troubleshooting" section of the following document:

[iTunes for Windows Vista or Windows 7: Troubleshooting unexpected quits, freezes, or launch issues|http://support.apple.com/kb/TS1717]

Before starting out on that, set the PC up to view hidden files and folders, as per the description at the beginning of the "User-specific troubleshooting" section.

*Some heads-ups before proceeding*

Be careful of any custom preferences (EQ, imports, etc) you have set up. Take a note of those, because rebuilding the relevant prefs returns all such prefs to their default settings. You may need to set up any such preferences all over again.

You may also need to reinstall any third-party plugins afterwards.

Things to expect during the pref file rebuild ... moving one set to the desktop (on XP) causes the setup assistant to run during the rebuild. Avoid saying yes if it asks you to import all the media files on your PC into iTunes. Otherwise, you'll end up duplicating all your content in your iTunes library. Moving the other set of prefs to the desktop (on XP) means that you have to agree to the licence agreement again.