I wrote a simple VB.NET application which works fine on the development machine.
However on another machine, even though the .NET Framework is installed, it crashes
It isn't that clear why PowerPacks is missing, the .NET 4 Client Profile could be an issue. There have been multiple versions of PowerPacks around and the version numbering got to be a mess. On my machine, that same version is reported as v2.0.50727, even though it is stored in the GAC as version 10.0
Best thing to do is to go back to your project. Click the "Show All Files" icon on the toolbar in the Solution Explorer window. That now shows the References node. Expand it and select the PowerPacks reference. In the Properties window, change the Copy Local property to True.
Rebuild and your build directory now will have a copy of the DLL. Copy it along with the EXE onto the target machine.