If you have another data cable (ribbon) you can try, that would be the first thing to try. One end of the cable will have a section with a twist in it...the boot floppy drive should be connected to that end of the cable. Some floppy cables have three connectors...the floppy drive you plan to boot to needs to be on the end connector. The other end, of course, goes to the floppy connector on the motherboard. Make sure both connectors are firmly seated.
Check the power cable, too. Remember that it's just opposite of the other drives...the red wire to the outside. It's easy to miss a pin on these connectors, so make sure your connection here is solid and you don't have a pin that's slipped under the connector.
Then let's look at the BIOS setup again.
In the Standard CMOS Setup: Check that Drive A is showing as "1.44M, 3.5in". Drive B should be "None" and Floppy 3 Mode Support should be "Disabled".
In BIOS Features Setup: Boot Sequence need to be "A, C". Swap Floppy Drive and Boot Up Floppy Seek should both be "Disabled". Floppy Disk Access Control needs to be "R/W".
If you find the cabling in good shape and all the settings in the BIOS are correct, it should boot directly to the floppy drive. If it still fails to initialize the drive, I'd be thinking the drive was bad.
As a side note, I have seen some brands of floppy diskettes that just wouldn't work for this while other brands would. I have no idea why this would matter, but apparently it does in some cases. Something to keep in mind...