Backing up/Creating a Windows 7 Install Disk?

My sister-in-law just gave me her worn out laptop. When she bought it, it came with Windows 7 installed on it already, and the cd-key for the copy of Windows 7 is on a sticker on the bottom of the laptop. She said it didn't come with any CD's or install discs or anything. She said she was "sure" so.. /shrug

Basically, I'm wanting to put Windows 7 on my desktop instead. The laptop has a cracked screen (among other things), so I was just going to salvage the copy of Windows 7, and the laptop hard drive, and toss the rest. The problem is, I have a perfectly good, unused Windows 7 cd-key, but no way of installing Windows (that I know of). I suppose I could torrent it? But that feels a little too sketchy for my tastes. I'm wondering if there is a way to just back up all the Windows 7 files off the laptop, and create a USB, CD, external HD, or something that could pull Windows 7 off the laptop, and create a bootable installation method. If that makes sense?

Anyone know if there is any way to do this? I know this laptop has "backup" methods, but I don't think I could back up the laptop, and then install on that on a desktop. On a completely different computer.

The laptop is a Toshiba Satellite something or other. I can give the exact model number if needed. Thanks!

Anybody? No?

I don't think there's a way to do what you're asking, but I was under the impression that Microsoft had ISOs readily available for download. I could very well be mistaken. Try hitting up a friend who has install media?

http://lifehacker.com/5832896/download-windows7-isos-to-reinstall-without-restoring-your-system

Digital River is a CDN that Microsoft uses to distribute their ISOs. Assuming your key is legit, and not one of those manufacturer-specific ones, you should be able to grab an ISO, burn it onto a DVD, and then install it using your key.