Hmm, if it's HP branded and slated to work for that particular laptop model, it should~ work, but there's always a chance they sent you a faulty one anyways.
irrelevant to your problem but yeah, your stories is what sparked my negativity towards HP laptops

My mom bought my dad a small HP laptop which was always hot for no reason. After a while (after warranty), it ended up slowing down and checking the CPU clock speed, it only ran at 50% always, never being able to use it's full CPU capacity. I took it apart to see if there's any dust and discovered that the GPU chip doesn't have any sort of cooling for it, no heatsink, no fan. I assume it overheated (probably what happened to your laptop back in the day) and damaged the nearby CPU.
I tell my friends not to buy HP, but they do anyways. One of them, their keyboard stopped working after it overheated and had to get it replaced. Upon getting it back, FFXI never played the same and would crash more than often. Another friend's built-in mic stopped working a few weeks after getting it. HP's high-end laptops might be nice, a 3rd friend has had 0 problems, but the low-end ones seem to be crappy. A 4th friend is getting a decked out HP laptop also -_-