What is the software version you're using? (Settings/About)

In versions before the current (2.2009.51-1) the phone didn't "wake up" when USB cable was connected, so couldn't go to PC Suite mode. I am assuming that by "on" you mean "screen on". If your phone is powered off completely, it should be fairly obvious it won't work...

Try updating to the latest software in Application Manager.

PS
I have filed a bug against the latest software as I do not think that plugging in a USB cable with screen off should wake up the phone. It should just start charging, as it was (often, but not always) the case in the previous versions.