This could cost you
Shibby,
When a drive dies, it frequently goes in stages. The first stage is where the computer's BIOS (or in your case, the USB auto-detect feature) can still recognize the drive but it is not allowing the OS to access the contents. Data from drives in this condition can often be recovered via software such as EasyRecovery™ DataRecovery 6.1 - Standard Edition from Ontrack. I have successfully used this software to recover data from a number of failing (not failed) drives. This is windows-based software only, so you'll need access to a PC to use it. The standard edition runs $199, but only you can decide if it's worth it. Note - you may be able to download a demo from Ontrack's web site to see if it will work.
Once the computer cannot recognize the drive, you're in the second stage where you're going to have to rely on someone else to get your data back. Ontrack is the only data recovery service I have used, and it's quite expensive. The last time I checked, the price started at $1,200 and went up depending on difficulty. I'm sure there are cheaper outfits available, but Ontrack is the best-known.
There are a number of "tricks" people employ to try to recover data, including putting the drive in the freezer (in a sealed plastic bag) for an hour or two and turning the drive upside down. I have never had any luck with these tricks, but you may want to give them a shot.
There are two points to keep in mind. 1) The more you mess with the drive, the more difficult it will be to recover the data if you choose to use a professional data recovery service, and 2) You need to decide how much your data is worth and make up your mind whether or not to spend the money.
Lastly, a comment. If this is a backup drive, why do you not still have the data on your laptop? If you are only using for extra storage, why are you not backing it up somehow?
I'm sure you've learned a valuable, if painful lesson - all hard drives fail, it's just a matter of when.
Good luck to you.