Alright so you've got a PowerFlyer in there as I suspected.
There is an extra lead that comes from the PowerFlyer hardware which connects to the standard Amiga IDE port. I *think* it's pin 28 if I remember correctly. The HD will still work perfectly without this lead connected - you just wont get any visible indication of it's activity via the Power Tower lights.
One thing I do need to clear up here, you say that the lights come on when the floppy drive is active?? I hope you're not saying that HD activity light comes on when the floppy is active? Becuase that can't be right at all surely. What you're probably saying is that the floppy drive activity light works but the HD one doesn't, is that right? If so, check the lead I was just on about - it's almost certainly the root cause of your problem, provided that the indication light itself isn't faulty that is.
BrianHoskins