Neil, which ports are your internal hard drives connected to? The drive for your OS should be plugged into SATA 1 Port 0. That is a red connector on the top row (towards the inside of the mobo) and all the way to the left edge. You should not be using the Orange SATA port (actually, it's an eSATA port). Start here and change as needed.
If you changed ports, go back and see if you can back up.
If you didn't need to make a port change or if the backup still fails, go into BIOS and change SATA Operation mode to RAID. Try the backup again.
Go into Device manager and look for a heading called something like IDE ATAPI Controller. Double click the SATA controller and post the ver# and date of the driver. Here are the drivers
for your board. If your installed drivers are the same date or older than what's in the link, I'd reinstall the Nvidia All in one driver and reboot.
There doesn't seem to be anything critical in the HD Tune screen shots. Some of those messages will always be there, but it doesn't necessarily mean you have a hardware failure on the drive side of things.