Making an image of the disk does not mean taking a picture of it. While not necessarily legal or allowed by the game publisher, there are programs that allow making a copy of a CD or DVD on the hard disk - this is called a disk image. The same, or other programs are used to then mount the disk image as a virtual CD. Examples of these programs include
Alcohol 120%
Clonecd
Game Jackal
Daemon Tools
Use of a disk image can allow the game to be played without the CD in the drive, or the ability to burn another CD if the original is destroyed.
If the disk is too damaged to image at this point, another possibility is to use a nocd patch or patched executable. These are hacked versions of the program that are intended to remove the need for a CD to be in the drive. The vast majority of modern PC games put all of the needed game data on the hard disk, and only use the CD to check if you own it. I personally find this annoying, since it means my hard disk space is used up AND I have to bother with the disk - one or the other please. I sometimes wish that PC games could also be just inserted and played like console games.
Patched/hacked executables are generally not allowed by the game publisher, and bypassing copy protection of any kind is illegal in the US (thanks to the Digital Millenium Copyright Act - DCMA, which incidentally steps on fair use rights and is therefore not very cool). There have been at least a few occasions where game publishers have actually encouraged the use of a nocd patch to overcome things like a copy protection system that only worked with Windows98, but not in XP. There was another instance I read about where a publisher released a hacker group's nocd patch as their own patch to remove the copy protection. Whoops!
One big caveat: many of the sites that host nocd patches also infect vulnerable web browsers with spyware, viruses, and trojans. Often, along with the nocd patch or hacked executable, an additional unrelated but infected program is included at no extra charge. Don't even consider looking for such a thing without a current and updated anti-virus, scan anything you download before running it, and do not use Internet Explorer.
Other (possibly questionable) options may include making a cd copy or image from a friend's NFS CD, or downloading a CD image from a file sharing system. Also be aware that with downloaded games from file sharing systems sometimes do not work, or have a virus included. Downloading copyrighted material may be illegal in some areas.
With regard to the scratches, there are products like "skip doctor", "game doctor", "cd doctor", or "dvd doctor" which are intended to repair disks by sanding the disk surface. Some stores that sell used games or dvds have one of these that they use on problem disks, so perhaps you can find a place that would be willing to run your disk through their skip doctor. Many game, music, and movie stores sell this kind of product too, but they are probably a lot more expensive than the game.
Incidentally, you can buy another NFS: HS on eBay for like $4.
Cheers!