SATA drive not detected at all.

Boot device sequence is not likely your problem. This sounds exactly like the 500 GB Seagate has significant errors. During the boot sequence the BIOS runs around checking that everything is OK and, in this case, gets error messages back from the Seagate drive so it tires again. And again. And again. And eventually it gives up and completes the boot process, but it does NOT show the Seagate drive because it can't respond properly.

Go to the Seagate website and look for their free diagnostic utility package, Seatools. I prefer the one for DOS that you burn to its own bootable optical disk and boot from. But you might prefer the Seatools for Windows for your problem. either way download and install it, then run all its tests on the 500 GB unit. NOTE that in one test it will give you a unique test fault code you must WRITE DOWN. If your HDD is bad and Seagate must replace it under warranty, they will want to know what these tests say and what that code was. Be aware that, if they do replace it, they generally will NOT offer to recover all your old files for you - you will lose them. So you will need to try some recovery techniques BEFORE returning a faulty drive.

Before you get too panicked, try one simple thing that SOMETIMES fixes things. Some SATA data cables slowly vibrate loose, so disconnect the power cord, open up the case and disconnect the 7-wire data ribbon cable at the drive, then re-connect it. Do this several times in case the connections are dirty. Then do the same for the other end that plugs into a mobo port. Then do the same for the power supply wires to the drive. Close the case, reconnect power, and boot up. Did it fix it? If so you got lucky and should celebrate. If not, proceed with the Seatools diagnostics.