You are legally entitled to create backups of all your media no matter what the EULA or the company's marketing try to tell you. That means you can create a working copy of every CD, DVD, Blu-Ray or HDD as long as it is only for your own personal use and you only use one copy at a time. No one can forbid you from backing up your data. You are even allowed to lend your game/album/movie to friends and family, as long as you do not profit from it. Again, it is understood that only one copy is active at the same time.
The legally grey area starts once you have to crack the copy protection of your purchased game to create your backup. Doing so means altering the code of the game, which is a violation of the Terms and Conditions you agreed to during installation. At the same time you as customer are entitled to create backups. I am not aware of definite precendents or judgements so if anyone knows more, correct me please.
What is casually termed piracy is in fact copyright infringement. It's still illegal but in a whole other area. Piracy is robbery at sea. Unless you obtain your cracked game by boarding a ship which is transporting them, you are not pirating anything. It's like calling jaywalking murder. Way out of proportion. At the same time, it isn't theft either. Please do not believe ads sponsored by RIAA and other similiar organisations. "You wouldn't steal a car"... meh. By definition theft makes the property unavailable to the rightful owner, the thief is taking something away. That's not the case with copyright violations. Otherwise you could download all Justin Bieber songs and rid the world of them because you took them away and no one else can listen to them now. 
That being said, copyright infringement is illegal and immoral, especially if you profit from it. Independent studies have shown that loss in sales is neglectable. I don't have the numbers available at the moment but I think it was something like less than 5%. Research on your own, it's an interesting topic.
Copyright infringement is the use of works protected by copyright law without permission, infringing certain exclusive rights granted to the copyright holder, such as the right to reproduce, distribute, display or perform the protected work, or to make derivative works. I think it is clear that reproduction and distribution are the main problems which means people who upload or host cracked games are clearly in violation of the law. The people who download the game are less so, it's a grey area again. Of course, if you use bittorrent, then you are always an uploader, even if it's just some kb.
Personally I do not use or recommend illegal downloads. I buy all my games, some even more than once. I have two legal copies of KotOR, KotOR2, BG1, BG2, Jade Empire, Dragon Age: Origins and quite a lot more.
Now let's talk about the initial, hypothetical question. You purchased the game and, in theory, could create a backup of your DVD (or whatever they use on the consoles). Since your original doesn't work, you could try to obtain a working copy... but... a cracked game would mean you'd be violating the EULA/Terms and Conditions and it's rather unlikely it would work for you anyway. The standard procedure with defect products is to demand the seller fixes the product and/or exchanges it for a working one. If they can't do so after three tries, you are entitled to get your money back. This may differ depending on the country you live in though.
TL;DR: Don't download an illegal and cracked copy, it's probably not going to help you and not worth the possible legal ramifications, even if you stay in the grey areas. Also, don't become a pirate. I don't think they have health care anymore.