Hi Joshua,
From your domain information, I find current name server point to GoDaddy, not Office 365 and no related DNS records for Office 365. In addition, the website hosted on GoDaddy can be accessed currently. If you would like to host mail service on Office 365 side, you need to verify domain first in Office 365. After that you need to point the name server to Office 365 side. Then you can choose keep your current public-facing website on GoDaddy. You can refer to the following article:
Update DNS records to keep your website with your current hosting provider
http://onlinehelp.microsoft.com/en-us/office365-smallbusinesses/hh335298.aspx
Thanks,
Johnny Zhang
