If you are in the US you can request a set of "backup discs" from Dell HERE   There is a charge but it's way less than buying a full retail copy of Windows.  If you are not in the US you will have call Dell for your area. You will need to have the Service Tag number. This is also a good lesson on backups.  I back up my entire hard drive (all partitions) to a separate hard drive, regularly.  If my hard drive would fail I can completely rebuild a new hard drive in about an hour.  The only data I've lost is since the last backup.  I use Acronis True Image backup software.    "Backups are not of IF they will ever be needed but for WHEN they will be needed.  
A few months ago, my hard drive had a mechanical failure and I had to replace it. My warranty was only one month expired at the time, so I shelled out the cash for a new hard drive on my own. When I went to reinstall windows, I realized I had lost my OS disk, and my only backup was on the hard drive that's burned out.  I'd really like to not pay 200 dollars for a product I've already purchased. I still have the product key on the sticker that's on top of my Dell tower. If I renew my warranty on my computer, is this something that Dell would replace for me? If not, am I completely screwed here? I'm currently running a 30 day oem just so I have a working computer.
How do I get my OS back?