On my home pc the MVC4 developer preview installed on my box but at the office I tried a few different times with no success.

Visual Studio 2010 SP1
It’s required for MVC4. Already have it on your box? That’s likely the reason WPI is failing to install.
Reading the log didn’t really give me much information but I was very sure that I had already installed VS 2010 SP1 on my box. Time to go around WPI.
WPI Installer Location
Aren’t sure where WPI installers are stored?

They are stored in your profile’s AppData\Local\Microsoft\Web Platform Installer\installers folder.
When I ran the MVC4VS2010 Installer by itself, outside WPI, the install worked.
Happy Coding!