If it is showing that it's still remapping data then yes, you should replace the drive. Easiest way to back up everything is with disc imaging software (which EVERYONE should use on a regular basis) - and by the way - you don't back up the bios - that's not stored on the hard drive. Here is something I put together a while ago to explain everything:
Disk Imaging software takes a "snapshot" of your drive as it exists at the time you create the image. You can then restore the entire image or any file(s) or folder(s) you choose. It is a virtually foolproof way of backing up your system and providing a safe haven in the event of a catastrophe that requires you to blow away your system partition and restore it to a previous state. It also allows you to "test" various software and be confident that you have a the ability to return to the prior state any time you choose.
I use Acronis True Image. It is the best of breed, but it isn't free. The best free alternative is Macrium Reflect.
1) I create an image of my system partition once a week to a second hard drive and keep the 2 or 3 most recent images. I also image my other partitions about once a month. I always enable "verify image" in the options. It takes a little longer, but insures a valid image.
2) I also create an image before performing any drive level function (ie, changing the size of a partition) or making any significant change to the OS (installing a service pack, upgrading IE, etc). Also sometimes before installing new software.
3) Images may be created on any medium (cd, dvd, external drive, etc). For obvious reasons they should not be stored on the same drive you are imaging. The best option is a second internal hd if you have one.
4) Images may be created "in the background" within the OS. If you need to restore the system partition, that will need to be done before the OS loads. You can start the process within the application in the OS and it will then tell you it needs to reboot to finish the process. Alternatively, you can boot to a "recovery disk" which you can create when you first install the software (or to the application disk itself if you have one). Other partitions can be restored without a reboot.
