I brought my WD External Hard Drive on May 8, 2011. On today, May 9, 2011, the hard drive is not working. The white light is on, but nothing happens when I plug the unit into my CPU. I did download files to the external drive yesterday, May 8, 2011, but I need to extract those files from this drive, because they were deleted from other sources. Please help

This is not an easy one. I guess you have to consider the fact that the disk is just bust.
I used to deal with great volumes of different disks for computer and servers. And even though it doesn't happen too often, every now and then, one of these disks fails in the first few days.
I guess even with the best quality control, such things can happen.

You could always try to disk with another PC to rule out the possibility that the PC is the issue.
If the data is really important, then you could contact the vendor to have a look at it. If it is just a faulty circuit board, then that can be replaced easily. But beware. If you just bring it in for repairs and don't tell them that you need the data, the disk will most probably be wiped when they test it.

Then there is also the more expensive option to contact a data recovery company that uses different specialized methods that allow them to get data back in even the worst kind of situations.