|Did you do an actual clean installation, a restore from recovery DVD set, or clone the old drive with its errors onto the new drive?|
Before installing the OS on the new drive, make sure that it is properly recognized in your BIOS.
Run Memtest via a bootable CD to see if memory errors are being reported as hard drive errors. Let it run through all tests. Any errors are cause for replacing the memory. Rerun the test for one stick of memory at a time to determine and confirm the bad stick. Modern systems run memory in dual channel mode and for that to run at its most efficient, memory should be replaced as a matched set.
Run the hard drive manufacture's hard drive test utility via bootable CD to verify the hard drives integrity. (Seatools for Seagate, etc.). This will give you the most reliable proof of a bad drive and the fastest possible way to get it replaced without charge. Original drives should be covered on the machines warranty for the first year (or extended period if you took that option) and other drives you purchased are covered by the drive manufacturer.
Assuming that your laptop is under warranty (Windows 8), contact HP support with the results of the tests if the memory, like the drive is bad (unless you prefer to purchase more or better memory anyway).
You have to be a little bit crazy to keep you from going insane.