|IDE ATAPI device = an IDE optical - CD or DVD - drive.|
(Also applies to at least some IDE tape drives, but you probably don't have one of those.)
Remove the AC power to the case and check the data cable that's connected to the IDE optical drive.
It is common to un-intentionally damage IDE data cables, especially while removing them - the 80 wire ones are more likely to be damaged. What usually happens is the cable is ripped at either edge and the wires there are either damaged or severed, often right at a connector or under it's cable clamp there, where it's hard to see - if a wire is severed but it's ends are touching, the connection is intermittent, rather than being reliable.
Another common thing is for the data cable to be separated from the connector contacts a bit after you have removed a cable - there should be no gap between the data cable and the connector - if there is press the cable against the connector to eliminate the gap.
80 wire data cables are also easily damaged at either edge if the cable is sharply creased at a fold in the cable.
Try another data cable if in doubt.
"Detecting Floppy Drive A Media"
That may or may not indicate a problem.
The bios may always generate that message, but you may not have noticed it because it was displayed too fast for you to read it when you were not having the problem that generated the ATAPI error.
NOTE that not all drive controllers support IDE optical drives.
Some older mboards have a second drive controller that's not built into the main chipset that cannot support the ATAPI standard, and, therefore, it will work with IDE hard drives but NOT IDE optical drives.
The mboard may have 3 or 4 IDE data headers instead of two in that case
E.g. if the second drive controller is a Promise one, it probably cannot support optical drives.
The same applies to the chipset of some older PCI IDE drive controller cards.