The DIY troubleshooter is basically the Microsoft Answer forum.
Submit a Request
You can submit a service request in the office 365 admin console.
Remote Connectivity Analyzer Tool
From here we can test Exchange, Lync, Office 365 and Free/Busy to test the online availability of other users.
Microsoft Connectivity Analyzer
Click HERE and then go to the client tab.
Use this downloadable troubleshooter to test connectivity of Outlook, lync mobile, Free/Busy etc. With this tools you can save the logs for the connectivity problems which is very useful.
Microsoft Online Diagnostics and Logging Toolkit
This tools has been deprecated.