Open an elevated (administrator) command prompt and run the following:
DISM.EXE /Online /Add-Package /PackagePath:C:\Features\Microsoft-Windows-NetFx3-OnDemand-Package.cab
Adjust the above command to wherever your CAB file for the .NET 3.5 package is stored. There are other command switches that may be used, but this is the most barebones solution I've found for using DISM to resolve .NET installation issues.

Try "DISM.EXE /Online /Add-Package /PackagePath:D:\sources\sxs" if installing from a mounted image. Replace "D:" with the correct drive letter.