Get new HDD and get computer running again.
Install whatever data recovery software you want to use.
Get a laptop HDD enclosure with USB converter.
Wrap old HDD in the new HDD's static bag and seal with tape. Then, put it in your freezer.
Wait 10 - 15 minutes.
Load data recovery software.
Crack your knuckles.
Remove HDD, unwrap, connect to enclosure, plug into laptop as fast as possible. Get recovery software going and pull off all that you can.
If you can't recover anything, get your checkbook out or just forget about the data. Data recovery from a dead drive is big $$$.
Finally, buy a backup solution of one sort or another.