Maybe this isn't how you do it in Windows 8 (which I don't own), but it's worth a shot.
Right click your taskbar, go into Task Manager. See if it's still running in the background, and if it is, terminate it. Wait a few minutes, then try and open it again.
If that doesn't work, try rebooting your computer and try to open it after that.
If THAT doesn't work, then go into "My Computer", go into your Program Files folders (if there's more than one on 8 like there is on 7, I dunno these things) and find the Paint Tool SAI folder. Go into it, and try opening the application starter from that folder (the actual .exe file).
If none of these things works, you might have to try re-installing it.