It would still work whether or not the HDD is faulty. The live CD doesn't require a hard drive. However, try to use a linux CD (Not live), but an actual distrobution where you can install the OS. If you can, then it's the recoveries which are failing to recognize the drive because the CD's don't have the HDD drivers on it (99.9% unlikely).
Eh, 3 months old? They will replace it free of charge under the laptops warrantee. If they refuse, tell them you are going to burn the laptop, their street advertisment posters, and the HP central office.