DO NOT buy that laptop. Those series were the absolute worse laptops ever made. A few members here had them and they got rid of them.
I personally have worked with them. They got tons of hardware issues, and especially heat issues, and taking them apart to fix them is even a bigger challenge because of the plastic being very easy to break.
Back to your question:
- Run MemTest86+ for 24 hours to check for RAM.
- Run HDTune for scanning the HDD for bad secors.
- Try to make the DVDRW read old copy and genuine disks.
- Move the screen up and down and see if there's any emptiness in the hinges. (HP's are known for having bad hinges)
- Make sure the licensed OS is installed.
- Use CoreTemp to check for temps.
- Fully charge the laptop and then use the battery until it dies, average battery life should be at least 2 hours.
- Test both speakers. Download a lossless (.wav) file of a really bassy song and check if the speakers stay clean sound wise.
- Check if the power adapter is the genuine adapter by feeling the build quality of the wire, plastic and also test its volts (If it over-volts by 0.5 it's ok)
- Check if the battery is genuine, The battery should have the manufactures logo on it.
Again, I really think you shouldn't buy that HP.
Can you give me your budget ? I can get you great prices.
Here's my list of laptops (Note that some are from PCandParts) Have a look a look at them. I'm sure you can find something.