Simply turning on your radio without the speakers hooked up won't hurt them. What will hurt them is is the speaker wires are touching each other because they're not hooked up to the speaker. This will cause a short, and usually will just put the radio temporarily into a safe mode, however it could have blown the fuse. Assuming this is an aftermarket radio, there should be a fuse on the back of it. You may have to remove the wiring harness plug to expose it, but it should be there.
A more likely cause of the problem, imo, is a short in the power wire somewhere that caused the fuse to blow.
Don, March 2009