Leon,
Since its external USB drive you can plug it in while computer is ON. It could be something in your BIOS (Basic Input Output System) that prevents it to load properly like boot sequence. But windows still can read it if you plug it in anytime you want since its USB drive.
If even then windows cant read it or gives you error make sure you unplug any USB device you have on your laptop/computer and try again to plug in only your external USB drive.
If still no luck then your external hard drive might be corrupted or dead.
There are many software you can use to try to save data from corrupted external or internal hard drives including thumb drives.
You can also try to plug it in someone else computer and see how it goes.
Read this, you will also find some suggestions of software you can use in the worst scenario:
http://www.popularmechanics.com/tech...o/tips/4294038
cheers