Peripheral problem?

That's quite normal. My optical mouse does the same. Although my keyboard leds do turn off.
The reason is that the keyboard and mouse are driven by the standby voltage of the comp, so you can turn the comp on using some keypress combination. (For my comp its ctrl-alt-backspace). Some bios has an option to turn it off. On some mobos there is a jumper that can be removed to disable standby voltage to the keyboard and mouse. But if your board has neither option you can't do anything about it.
You may want to check that you do power off and not just make some sort of standby or suspend to ram etc.

<i><b>Engineering is the fine art of making what you want from things you can get</b></i>