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If the COA sticker with Product Key is not on bottom of laptop, then it is under battery on Dells.
Make sure key is readable in which case you can Clean Reinstall - Factory OEM Windows 7.
Everything you need is in the blue link.
However because of the HD diagnostics done already you should first confirm if the HD is bad and replace it if so. Run Dell Diagnostics again to see if it will complete: Dell Diagnostics Utility - How to Run the
If not download the WD Data Lifeguard DOS CD ISO to burn to CD using Windows Image Burner or ImgBurn, boot it to run the Extended Scan. If it will repair the HD, then confirm this by running Disk Check on all partitions and the Dell Diagnostics again.
If these all fail after best efforts then replace the HD and clean reinstall using the steps in tutorial. Google for HD or SSD replacement choices for your model.
You will get the best performance boost available by replacing with an SSD if you're interested.