External HDD units are ideal for backups. You can copy to and from them, disconnect when not in use to protect from all sorts of threats, and move them offsite for storage. Of course, you actually have to DO what is possible.
OP, your last post suggests you have not made a backup to your external drive; it sounds like you simply moved all those files to the external. If that is the only copy you have of them, I agree getting a second external to be used as a proper backup unit would work well.
You can't copy to your DVD writer? Well, there are two things you need to do that. One is to recognize the size limitation. A DVD-R can hold about 4 GB of data, so you can't just dump more than that on one disk in the drive. But how you put it there is important. A DVD drive is NOT like any hard drive, and not even like a huge floppy unit. You can use software like Nero to burn a defined collection of files onto a DVD-R disk. OR you can use a utility called InCD (comes with Nero and some other packages) that installs itself like a driver and allows you to drag files to an optical drive (just like dragging to a hard drive) and add it to that disk. But you do need to use one of these software tools - Windows itself does not do "drag-and-drop" with optical drives.