If Windows can show you something of the old HDD in My Computer, then it MUST be detected by BIOS, AND it MUST show up in Disk Management.
So, first let's check the IDE installation. You have one IDE port on your mobo, and one IDE HDD plugged into it. Any IDE port MUST have a Master device if it is to operate, and this is set by a jumper on the back edge of the HDD. Use the diagram on the HDD unit itself to tell you how to set the jumper to Master or, if it exists, Master with No Slave. Now plug into the HDD the END (Black) connector of the 80-conductor ribbon cable. (Yes, 80 wires in it, but only 40 pins on the connector.) The other end of the cable with the Blue connector plugs into the mobo IDE port.
Next, check BIOS Setup for where the IDE port is configured. Are you sure the drive is not there? If it is not, perhaps the detection process is wrong. Many BIOS's have a separate screen where you can force it to do a more thorough HDD detection if it failed the automatic process. Look for that.
Next, check the BIOS for where you configure the floppy drive port. Since it appears you actually do not have one, DISable it. MAYBE it is trying hard to get a response from a non-existent drive. If you make any changes in BIOS Setup, don't forget to SAVE and Exit.
In Disk Management on the right there are two panes, and EACH of them SCROLLS so you can see all they contain. The upper right one shows you all the devices Windows understands and can use, and your IDE unit ought to be there if it can be "seen" in My Computer. But look closely at the LOWER RIGHT pane. The IDE HDD ought to be there for sure if BIOS has detected it. Check whether its size is correct and whether it has a any Partitions on it. Each Partition should have a letter name assigned to it already. If it does not, you can RIGHT-click on a Partition and choose a letter name for it. If you do that, back out of Disk Management and reboot so Windows can update its Registry.