As realblackstuff mentioned, connecting the drive to another computer is the best way to back up your stuff.
There are two good ways to do it. You can use a 2.5" to 3.5" drive adapter, to connect your laptop drive to a desktop system. From there, you can copy your data (hopefully).
The other way is using an external enclosure, such as a USB or Firewire housing. This will make it pretty easy for you to connect your drive to just about any computer and copy the data.
Of course, there's a good possibilty you won't have enough time to copy the data. I've seen plenty of drives simliar to yours that will only give you a few minutes at best, then they start clicking etc... Which makes retreiving datta nearly impossible.
The trick is to place it in a freezer first. What I do is place it in a static bag, wrap it in a small towel and place it in the freezer for about a day. When you pull it out of the freezer, immediately hook it up to your system and copy the data. It should work much better - maybe even perfectly - and you'll be able to get your data off.
I don't know the science behind it, but it works very well for drives damaged by physical shock. I've used this several times, and nearly every time it has produced positve results.