You want/need to get this VERY HANDY little Item:
Newegg.com - Rosewill RCW-608 USB2.0 Adapter For IDE/SATA Device (Include Protection case) - Adapters & Gender Changers
Pull your laptop harddrive out (or ANY harddrive for that matter), attach it to the above adapter, then plug directly into the USB of your Desktop (or other laptop) computer.
Provided the drive itself is not completely shot (if it is still functional) then you will be able to transfer the data to another computer or Disk.
Using the above adapter ANY attached harddrive (IDE, SATA, Laptop) will show up as an extra drive on the computer you plug it in to.
Very Handy.
If the drive is completely SHOT, Finito, Non-Functional, D-E-A-D, No Work, Kaput...then your only option is to send it in to a specialty company that will charge you thousands of dollars to recover the data.
You can get an Idea if the drive is still servicable by going into the BIOS of your computer. If your drive shows up (and give stats in the bios) then you can probably recover your data.
In any case for $25 you will have a very handy tool.