As jsc has already mentioned in the first phrase, "run light comes on and never goes off" indicates that the floppy connector plugged into either the floppy drive or the motherboard end has been reversed. Unfortunately some floppy cable are not keyed (notch in the middle) like IDE connector is, or the connectors on the ribbon are keyed, but the floppy drive itself isn't (just open pins).
The floppy connector on modern motherboards are almost always keyed (to accept the notch).
If you've reversed the connector and the same problem persist, try the 2nd floppy connector, the connector after the 'twist' in ribbon has been made.
It's been a while since I've used an internal floppy drive (got a USB one now), but I seem to remember all my floppy drives only works after connected to the 2nd connector.