Rob is having an issue with his computer hanging only while Microsoft Outlook is open. Outlook displays his Exchange and Gmail accounts. He's tried several things, including running Outlook in Safe Mode, disabling his antivirus, and turning off add-ons. Leo says to look at the connection as it syncs. He should try changing the polling times. It also goes through the messages and indexes them, but he started with empty PST files which dramatically changes the time it would take to index them.
Rob should try uninstalling and reinstalling Office. He might even want to try reinstalling Windows. He can try turning off the Exchange download, too. He should do the simple stuff first and work to the most problematic. But Outlook is definitely the culprit here.