Construct 2 should run fine without admin privileges. You can even install it from the setup program without admin privileges!
If it's Windows 7 that's a bit surprising, my first guess would be it's an out of date version of Windows XP that isn't supported, but W7 should be fine. My next guess is the graphics card drivers - it might help to update the drivers, but you definitely can't do that without admin permissions... hmm!