I have not experienced such a problem before, did you check the bios ?
Normally this is where you would configure what kind of FDD is assigned to a: and b:

You probably need a floppy cable with a twist in it. A drive is at the far end of the cable from the motherboard, past the twist. B drive is in the middle (between motherboard and twist)

Some 5.25" drives have a DS (drive select) jumper on them. Most 3.5" drives are hard wired to DS2. The twist in the cable actually swaps the drive select lines so if both drives are set to DS2, the one after the twist will be changed to DS1. So if you have a cable without the twist, in order to use your 5.25" and 3.5" drive on the same cable you must change the jumper on the 5.25" drive to DS1. DS1 is recognised as A: and DS2 will be B: so make sure you set them up in the BIOS setup correctly.

(To confuse matters more, some drives have DS0/1 instead of DS1/2, set your drives accordingly)

I find it's easy to plug the cable in the wrong way on either the 3.5" or to the motherboard. When I get FDD problems on a new setup I always try reversing one or both of the connections as it's not always crystal clear how they were meant to go in the first place. Also check your BIOS for floppy configuration - sometimes there are options for type [like 1.2mb etc.] which if not set correctly will fail. Trial and error is your friend here..