Outlook often stalls just before completing email downloads. Upon shutting down Outlook to re-open it won't open. A restart of the computer is usually required to make it work properly.

Outlook 2007 is fully compatible with Windows 7, both 32-bit & 64-bit, so it's not a compatibility issue. Try running Office Diagnostics:
Open Outlook.
Click Help > Office DiagnosticsIf that doesn't fix it, back up your PST file and re-install Outlook.
Do you get the problem in Safe mode? Hold the ctrl key down when you click on the shortcut to start Outlook to run in Safe Mode.
