The 10,000' overview of how I usually approach it.
If the laptop is my only computer, Buy a replacement HD and install it, reinstall windows and get a running system.
Buy external enclosure (USB) for the failed drive and install it in the enclosure.
See if it can be mounted. 9 out of 10 times it can, and I pull the data off.
If it is clicking or grinding and doesn't want to mount. I put it in the freezer overnight (in a ziploc bag with a packet of silica gel, so it doesn't frost and condensate when it thaws later).
Take the iceberg drive out, plug it in and try again.
If these are a no go, and the data is that important, then $1600 is not that unreasonable for true physical data recovery. To be done properly it often involves a clean-room environment, identical hardware (large inventory of drives/parts/controllers/firmwares for all the variations), and pulling the platters out surgery style.
ETA: Don't pay too much for the enclosure (sub $20 if you shop around).
Here's one from Monoprice for about $10