I don't think I have seen this one before, so we had better start with basic principles.
1) does Quicktime work normally? iTunes will not work if Quicktime doesn't.
2) open the task manager>processes tab and try to start iTunes. Does iTunes.exe appear and if so, does it go away or does it remain although iTunes does not open?
Then if Quicktime works, try following this troubleshooting method.
http://support.apple.com/kb/TS1421
The first step in the method is to find out if the problem is specific to one user or system wide.
The system wide troubleshooting refers to malware, malware is an important source of trouble with iTunes and you need to be sure that your system is clean.
It would be a good idea to download malware bytes and run as full scan, it is free.
http://www.malwarebytes.org/