Hi Paul
Not wishing to disagree with Keith, because that can be a good solution. But depending on what's wrong with the drive and how scrupulous your local IT company is, you could spend far more money on this option.
I don't know how computer savvy you are, but this is what I do in your situation. Carefully unscrew the external hard drive enclosure and take it apart, so you're left with a standard hard drive minus the power/ usb attachments etc.
Then install the disk as a secondary device in your PC, or buy a USB-SATA (or USB to whatever connector your drive has) and simply plug it into your computer. If the drive is working, this will allow you access to your files. You should be able to buy a half decent connector for a tenner. If this method fails, the computer shop is the next step.
Let me know if I can be of any more assistance mate