|"Sometimes the data cable being on backward......" on one end connector ".... will keep the light on. But if it's on backward the drive won't work"|
"The red striped edge of the cable should be connected to the # 1 pin side of both the drive and motherboard connections. Make sure it's connected that way."
On the floppy drive header, the stripe is usually next to the power connector when the cable is installed correctly.
You use the end connectors only, not the middle connector on a 3 connector data cable, for the single floppy drive.
If that's all correct, then it's likely you have a data cable problem.
It is common to un-intentionally damage data cables, especially while removing them. What usually happens is the cable is ripped at either edge and the wires there are either damaged or severed, often right at a connector or under it's cable clamp there, where it's hard to see - if a wire is severed but it's ends are touching, the connection is intermittent, rather than being reliable.
Another common thing is for the data cable to be separated from the connector contacts a bit after you have removed a cable - there should be no gap between the data cable and the connector - if there is press the cable against the connector to eliminate the gap.
Try another data cable if in doubt.
Installing software should have no effect at all on whether the floppy led is on or off.