Yes, if your floppy or hard drive cables are on backwards, their lights will stay on. Don't leave a computer running liek this-my stepson did and damaged the on-chip controller, ruining the motherboard. The floppy cable always goes opposite of the hard drive cable on the back of the drive, BTW.
Also make sure you do not have any mounting post sticking up where there are no screw holes in the motherboard, or you'll short out the motherboard. This rarely results in permanent damage, but could, depending on which circuit is grounded.
Cast not thine pearls before the swine