Hi Jeremy,
Based on you situation, please check your software whether it meets the requirements for Office 365. Please refer to the following articles:
http://onlinehelp.microsoft.com/en-us/office365-enterprises/ff652534.aspx
http://technet.microsoft.com/en-us/library/cc263526(v=office.14).aspx
Meanwhile, I recommend you use IE 32-bit version. You can check whether the IE on your desktop is the same version as in your laptop.
Thanks,
August Sun