Install Visual C++, or C whatever runtimes. you need it for powdertoy to run. if this doesnt solve ur problem download de DLL and put it on the folder where it's supposed to be on(Google FTW?).
One way, as henry700 said, would be to install the Visual C++ 2010 "redistributable" package on your new computer. You can just Google "visual c++ 2010 redistributable", and it'll be the first link there.
Another way (much easier) would be to just copy C:\WINDOWS\system32\msvcr100.dll (at least that's where it is on my Windows XP computer) into the folder where the .exe file of your mod is.