It depends upon how bad the HDD problem is. If the drive won't boot, it sounds like the drive will have to be pulled any way we look at it. Definitely don't write files to the drive or format it as that makes the entire process more difficult (if not impossible...well...with enough money it's still possible).
If the drive spins up:
* pull the drive
* plug it into another computer as a secondary drive
* since it's a notebook drive you'll need either a 44-pin to 40-pin IDE adapter to put it into a desktop computer or...
* my choice would be a
USB-IDE adapter then you could plug it in as a second drive to a notebook or desktop
* the drive should simply show as another drive letter, then drag and drop files to the good drive
If the drive spins up, but your OS doesn't recognize it or gives errors instead of showing you any files, then I'd say it'll be a couple hundred dollars for a shop to pull data off of it.
If the drive doesn't spin up...yeah...that's some bigger money...maybe over a grand or two and those files better be quite valuable. It can still be done...recovery companies were pulling data from fragments of hard drives from the WTC after 9/11. But that's thousands of dollars.