Sorry to hear about your backup drive dying! A couple things about that though.
First, by definition a "backup" should always be a *copy*, not "a place I put data I don't need right now". Otherwise, as you found, if the *one* place that data exists does fail, you lose the data, and it's not really a "backup".
Second, with external drives often what fails is not the drive itself but the IDE or SATA to USB board inside the drive enclosure, or even the power supply, or fan, or other things. In some cases you can simply open the unit up, get the drive out, and plug it into your main computer directly through the internal connections and get your data. If it's one of those ultra small, portable, USB-powered drives, then it's using a small 2.5" laptop hard drive. Those you usually have to connect to a laptop as a second drive or replacement drive, unless it's newer and SATA in which case it will connect just like a normal SATA drive. You can also get adapters for 2.5" IDE laptop drives to connect to your internal IDE system.
Hopefully that helps.
- Oshyan