How can I play an XBox 360 game if the disk is unreadable?

No, there is not a legitimate way to download the FIFA 14 install image from the internet to load it onto your Xbox 360.

Once the "Donut Ring" scratch has been burnt into the disc, it can very frustrating to attempt to get the game working as you every time you attempt to, it gets further and further into the game before rejecting the disc and saying "Disc Unreadable", however it is a very low possibility you can recover disc data from that disc.

Is there a way? - Of course!

Attempting DIY is an option and worth trying because at the end of the day, the disc is not going to work by itself, but in your circumstances I can see the problem. My suggested options, although they may not apply in your location:

In my local area with GAME, if you purchase a game you have up to 14 days to return it as long as the product is in the same quality and standard as when you purchased it. Therefore I have done this in the past and although it is frowned upon, has no real harm. Purchase a pre-owned FIFA 14 from a store and download it, after the download is done try your FIFA 14 and if it works Hoorah! Just return it with the excuse that your console can't read the disc.

If that isn't an option for you my only other suggestion in your case is to buy the game again, annoying but we have all had to deal with it. Personally I have had to experience this around 14 times, every single time the same reason; I charge my controller using a play and charge kit, wire wraps around my foot and as I stand up my Xbox console launches off the desk. However reality is reality and we all have to face it, some of us are more lucky than others. However, if you don't feel like buying another FIFA 14 due to price, purchase another game for a lower price to keep you entertained until the price has dropped.

Really hope this rambling has helped, just a few suggestions for you. Really hope it all works out for you!

Rent a game from an internet site like lovefilm, that way they post it to you and then you return it in a certain amount of days. Either that, or find a disk image somewhere (obviously you cant get a legit one) and burn it to a dvd (Tesco ones are best)

Hope this helps!

You actually can repair your disk using something called a "Disk Doctor" or a "Skip Doctor."

A disk doctor is a combination of a special resurfacing spray and a buffer (can be motorized, or just a brush that you rub the CD with)

The idea is that the actual data on the CD is burnt in very deep, but scratches and other stuff tends to only be on the surface. You can therefore "buffer away" the surface scratches, returning your disk to as good as new.

I've tried such technology before and I can say that, at least in certain situations, it absolutely works.

Here is one I've found that is affordable. I make no warranties as to it working:

http://www.amazon.com/SkipDr-Manual-Disc-Repair-System/dp/B0015ACUKC