I ran into the same issue a while back with my cab.
In my case, I'd powered the LEDs via a USB port on an auxiliary USB card. It just so happened that that card supported what it called "USB Charging".
What that means is that even when the PC is off, there's voltage on the USB port. This is so you'd be able to charge whatever is plugged into the port even though the machine is off.
For some things, that's great. But if you happen to be powering lights with that port, it's not so great.
The easiest thing to do is not use a USB port for 5vdc. Instead, use one of the power cables that come straight out of the powersupply.
There MIGHT be a bios setting for selecting whether you want the usb port powered or not when the PC is off. Mine didn't have that.
You can also try switching USB ports. I've found that even in the same machine, the ports behave differently. In my case, the ports for the FRONT of the machine stayed powered up. Those in the back did not.