Re: Galaxy S3 won't turn on after trying to backup with CWM
If not, you can download one at
SamMobile Firmwares (you'll have to create a free account to download a file.) Enter the model
number (like i747), not the name (S3). Choose the correct country/carrier. You'll install it using
Odin.
Press Volume Down and Home. While keeping them pressed, hold the power button until the phone starts. You should get a screen telling you to press Volume Up to continue or Volume Down to boot normally. Continue, and install the stock ROM. (The phone has to be plugged into the computer you have Odin running on. You have to unzip the file you download from SamMobile - it's easiest if you put the files you get from it in the same folder that Odin installed to.) There are hundreds of Odin tutorials on the web - choose your favorite one. (After doing it once, you'll be able to write one - it's that easy.)
If you can't get the phone to respond at all (that's called a hard brick - a soft brick means that it foes something, but it doesn't work), you'll need a Samsung Dongle. (Look samsung dongle up on eBay, click the Buy it now tab, sort by price and you'll find some for a dollar including shipping.) Remove the battery for about 10 seconds, then replace it. Plug in the dongle (it goes into the charging port). After a few seconds, the phone should be in download mode. Remove the dongle and plug in the cable going to the computer.
If the dongle doesn't work, the motherboard is probably bad. Get a repair estimate first, but you might find that's it's a better idea to buy a good used phone on
Swappa. (Never buy a cellphone on Craig's List or eBay, unless the exchange takes place at the carrier's store and they register the phone to you as you pay the seller.)
Edit:
To restore a nandroid backup you need the recovery that made the backup (unless it's in a self-installation package). TWRP won't restore a CWM backup and CWM won't restore a TWRP backup.