STOP using your compaq, and clone its HDD ASAP. Do this BEFORE it fails.
When HDD failure happens, it's usually sudden and fatal.
Since your computer is still running fine, then your best bet is to ignore those silly re-install discs, and instead buy a new HDD, then make a bootable bit-for-bit copy of your existing HDD onto the new one. I've done cloning MANY times, and didn't need to reinstall anything. It's also a good way to expand your HDD capacity at the same time. It's also great for making a backup of your entire HDD contents (eg, another spare).
Step 1: buy a new HDD
Step 2: Power off, and attach your new HDD into your computer. Best to use the spare socket inside your computer, but otherwise you can use any external HDD enclosure that attaches via USB. Internal one has much faster copy speed.
Step 3: download & run a special program that clones your old HDD contents onto the new HDD. See added info below.
Step 4: Power off, and plug your new HDD in place of the old one.
That's it! Your computer will run exactly as before. Your new HDD is an exact copy of the old one, plus it has extra unused space (new is usually much bigger than old).
There are many freebie HDD cloning programs available from HDD manufacturers. Most (all?) of them insist (& verify) that you have THEIR brand of HDD attached somewhere on your computer (either inside or inside an external enclosure). Eg, My favorite is MaxBlast3, by Maxtor. Another is Acronis TrueImage, by Seagate. Another is Clonezilla (not from manuf). Youtube has how-to videos, if you need. The CD containing cloning S/W is sometimes inside the retail package with your new HDD.
The cloning program is OFFLINE, meaning that it's on a separately bootable CD, and NOT running within Windows. You reboot using the cloning CD instead of booting Windows, and it walks you thru the process. It's all automatic, and you simply choose the SOURCE and DESTINATION Hard Disc Drives (HDD) with your mouse.
Lastly, if your HDD is failing, then all downloads & burning of your cloning CD (if any) should be done on ANOTHER computer. Your failing HDD should be OFF, and spun up only when you're ready to clone it.
BTW, cloning avoids having to deal with Windows (& other) license keys. Whatever was on the old HDD is on the new, in SAME form (eg, O/S, your photos, files, etc. remain as-is). So no need to reinstall anything, at all. OTOH, recovery discs to reinstall Windows will force you to reinstall everything from scratch (total PITA).