Sorry for the delay...
The Floppy for that should be OS8. But that can be difficult to make. As for the floppy being spit out, it could be the disk is bad or the drive's head is broken, as in the past people used to take a pair of pliers to a stuck floppy and yank it out, ripping the top read/write head off its mounting. So it is not a ROM problem. Only way to be sure is to remove the floppy and remove its cover and inspect the top head. Much easier to just swap the drive with a working unit!
I think you can turn the unit on as a SCSI Drive and connect it to another Mac through the SCSI Port and inspect the drive like modern Macs can connect by FireWire Mode, but I forget how that is done. If you put the drive in a 5300, format it and install a system on it, it may not be compatible to the 3400. In the least it should be OS8 for the 3400. I still think its a partitioning and formatting problem.