Can you? If you have the right model, yeah...
Generally Laptop drives are 2.5" PATA, but many are switching over to SATA... You'll also want to contact the vendor of your laptop.. they may be able to replace the drive.. you may need another copy of your desired OS.
If you got a Dell or HP/Compaq, they're usually pretty helpful within the barriers of allowed assistance (e.g., warranty status).
Obviously that won't help your data, tho. We're in a similar boat with one of our drives. There are lots of little tricks that apparently work (haven't tried them) such as freezing the drives, dropping them a little (reseats the heads).. yadda yadda... you could take it to a professional... it could be pricey unless it's a simple fix (can't really tell yet).