PS3 hard drive data is also encrypted to the system as well, making a simple swap impossible. Thanks SONY!
If you're game to try a little questionable stuff on your PS3, you can try the hair dryer trick to get it up and running again for a short period to copy all the data off. Essentially you run a hair dryer pointing at the back vents to really poorly "reflow" the solder for the system chips. It's hit or miss, but I've helped 2 different people recover their files this way. Just do a bit of googling about the hair dryer trick and you'll get a better overview of what I'm talking about.
Note however, don't consider the hair dryer trick even a semi permanent fix. Get it going, get your files off quick, and then stop using the system. You need a proper reflow or reball to fix the YLOD issues on the PS3.