The first thing I would do is to check them on a different machine. You can definitely get the data off that way. If they work just fine on another then you have a software or hardware problem on your PC. With your PC seeing the files on your MP3 player, but not HDD's makes it sound like a hardware problem with your HDD's, but I can't imagine both going out simultaneously. So let's go ahead like that is not the problem for right now.
Are they 2.5 inch or 3.5 inch external drives? Like the 2.5" laptop style drive, the 3.5" desktop style drive inside the external case requires 5 volts DC which is provided through the USB port. The 3.5" drive also requires 12 volts DC power for the drive, which it will generally need to get externally. If they are 3.5" drive I would check their separate 12 VDC power supply.
If there are 2.5" drives , in those external cases or the external power supply is working fine, then you're looking at a problem on the PC side. Right click on My Computer, in the start menu or on the desktop, and select manage. Under Disk Management you should be able to see all the drives that the PC hardware is able to see, whether or not Windows can see them.
Be careful here, you don't want to initiate any drive or do any other operations that may destroy the data on the drive.
Note all the drives and their sizes (the CD/DVD drive won't have any additional info like the HDD's) that are present and close the program. Now hook up one of your suspect disks, wait until the PC has picked it up (maybe about 45 sec to a min), then open the the Disk Management program again and look for any additions, you may need to restart the PC with the drive attached. Do you see either of the drives now?
If you can see it and it says it's healthy, you can assign it a different drive letter, to ensure it isn't conflicting with another drive. Go way out and pick something like an (X) drive letter or similar. Don't do anything other than that or you could lose data. If you still cannot see it, or it says it is uninitialized, then they sound like they maybe hosed. Whether that is the controller in the external case or the drive itself will be what you need to determine.
You can take those drives out of their external cases, although the process is liable to damage the case at least cosmetically, and place the HDD's directly on an internal SATA or IDE connection and power. I have some more steps to try, but you should establish whether it is a hardware or software problem first. Tear out should be one of the last resorts.