DOS drivers have nothing to do with boot from floppy.
In order to troubleshoot the problem do several steps:
1 - create a Startup floppy and check it on another machine that it is bootable;
2 - double check the drive boot sequence and other floppy related settings in the BIOS (yes, again);
3 - try BIOS default settings;
4 - replace your floppy drive with another from 100% proved working machine and try it with 100% proved bootable diskette. But first check that everything works fine on another machine, then reinstall.
If the floppy drive from another machine also doesn't boot on your computer, put it back, check on that another machine again, ensure that it works as before, then let us know about still a problem on your computer.
Or, while you are checking the hardware, install your floppy drive on another machine and try to boot from floppy there, check whether it works. Or better just swap the floppy drives and see how you are capable to boot from floppy on either machine. Let us know anyway.