Windows 8/8.1/2012 and .NET 3.5 installer problems.
If the standard methods for installing the .NET 3.5 platform are reporting errors (that they can't access the installation source files and they can't be downloaded from Windows Update either) then there are three updates that probably are blocking the installer. These are KB2966826, KB2966827 and KB2966828. Removing these updates and then using the standard methods should succeed. You may then reapply the updates (and the new ones that .NET will require) to secure the machine.
Update: Microsoft has provided a fix for this problem at https://support.microsoft.com/en-us/kb/3005628 (note that the .exe version did not work on our test machine, but the .msu file did).
Update2: This is another issue that can cause the same result... http://www.askvg.com/fix-cant-install-microsoft-net-framework-3-5-in-windows-8-and-later/
This new issue is a problem with WSUS updates and can be fixed via gpedit.msc, Computer Configuration -> Administrative Templates -> System -> Specify settings for optional component installation and component repair. Change to Enabled and check "Contact Windows Update directly..."