I'm afraid I can't
It is one of two things, since you've tried everything humanly possible except throwing it out of the window...
Since the other one suddenly stopped abbruptly, and the new one doesn't work either, it is rather worrying.
I would replace that one as soon as possible and test it. if that new one then doesn't work
(and you do have the cables the right way round now, if the light doesn't come on or not. It wouldn't have worked the wrong way round, and that light was a warning that something was up. At worst, having the cables the wrong way, it could cause the PC to run slower at bootup)
So yeah, get a new one (hopefully that ones dead too) and then plug it up the same way.
If it doesn't work, i'm afraid to say you probably have a faulty Floppy connector on the motherboard adn I wouldn't know what to do then.
If you look inside the floppy slot where the ribbon goes into the motherboard, are there any loose pins? Are any bent? Are any even broken off?
These could be answers, and might be able to be salvaged if they are just bent, or maybe even loose. I would have no idea what to do if some were missing.
If nothing seems wrong there, it is something deeper into the slot, and needs either a PC technican, or a new motherboard
But seems pretty stupid just for a floppy drive to have to do that...
Any way you could get around the problem by buying a USB drive? These can have 64mb, 128mb, and even 512mb on one chip able to transfer data from one PC to another if you really need it, and this is a better soloution.
What you need the floppy disc for though, could you place it on something else for example? Like a USB pen drive like i mentioned above? They are rather cheap now too