I encountered the same problem today: my iPhone 4 suddenly stuck on "Connect to iTunes" screen and iTunes did not recognize my iPhone 4 when I plugged in via USB (i.e. I can't update or restore my iPhone 4, and I can't enter the DFU mode). When I pressed the sleep and home button, trying to reset it, I can't as the "Connect to iTunes" screen kept popping up.
After I did some research on line and tried many ways, I finally found something that fixed my problems:
1. check your computer to make sure that you have "Apple Mobile Device support" (Control Panel -> check the "Uninstall a program")
2. Disconnect your iPhone from your computer and close iTunes
3. Go to "Apply Mobile Device Support" --> "Stop" it and then "Start" it again.
4. Re-start iTunes and connect the iPhone 4 to the computer
5. Select "Restore" --> and my computer showed a screen in the line of checking Windows on installing "Apple Mobile Device Support" USB (I can't remember the exact words, but it's re-activating your "Apple Mobile Device Support")
6. Once "Apple Mobile Device Support" is re-installed, the "Connect to iTunes" screen went away and the iPhone is being restored to its factory setting
7. Let it run through the course, and you will be asked to re-log into iTunes (where you can backup all your files).
8. Backup your phone and it should solve the problems.