So how did you transfer the Operating System and data? What OS are you using? Is the new drive type the same as the old one (IDE, SATA etc). Old HP often had (say) XP and a restore partition, which was used for the boot files of XP, so they were not actually on the OS partition at all. You will need to clone all the partitions if that is what you are doing. Another potential problem is HP were pretty strict about pirating, such that the OS can be tied to a particular model or type of Hard Drive.
Chances are you will need to talk to HP, quote the PC model number and ask how do you replace a failed HDD?