You might be in a bit of a pickle.
There a number of things I gleaned from your question. Most of them are bad news. A possible glimmer of hope: you said you have your important stuff on external drives that you back up regularly. If you meant that you’ve been doing full system image backups, you’ll probably be fine.
Backups to the rescue?
When you say you back up regularly, how do you do so?
If you’re doing a full system image backup, which is what I recommend folks do (at least periodically), then to put it bluntly, you’re golden. You can replace the drive, boot from the backup software rescue media, restore the image backup; and you’ll be off and running.
But if you’re not doing that, then the news is grim.
If the disk doesn’t spin, time to pack it in
If the disk isn’t spinning, then it’s dead, absolutely dead. You can’t reformat a drive that doesn’t spin.
The fact is, you and I can’t even recover data. A data recovery service perhaps could, but you and I cannot.
Most of the recovery discs, like the ones it looks like you have, rely on a pristine copy of the operating system that’s stored on a hidden partition on that hard drive disk. That means that the recovery discs you have in hand have no chance of working.
You have two options. Some manufacturers will send you a true installation disc if you contact them with this problem. Some will only do it, of course, if you’ve actually bought the replacement hard drive from them. Contact the manufacturer of your computer, or the retailer from whom you bought it, and see what options they’re willing to provide.
You could get lucky. If you don’t, then your only one real option is to get the installation media yourself.
In your case, that means purchasing a copy of Windows 7 retail and installing it from scratch once the drive has been replaced. Of course, you can also consider another operating system like Linux, which is free. But to get back to something close to what you started with, you’ll need a Windows installation disc.
And I strongly recommend that you start a periodic image backup of your machine to avoid disasters like this in the future.