You have a Bootable backup disk.

Boot the machine using this backup disk

Do you have drag and drop now?

If the answer is Yes, then you have a slightly corrupted system that you may want to replace.
This can be done easily, and safely, with the aid of the OS X installation disks. All you need to do is an Archive and Install.
Do NOT proceed with the install unless you see, and have checked, the Archive and Install option in the installer.
Failure to do so will result in the loss of ALL your data.

If the answer is No, then you have something else going on there, possibly hardware related, but that would be the subject of another thread. (post)

Good luck, let us know how you get on

P