I recently broke the screen on my s3. Instead of paying the money to have it replaced I did it myself with the kit from ebay. During the removal of the old screen I nicked the menu button and after replacing screen it refused to work properly. While trying to find a soft key app for my rooted phone which would take over the menu function I edit a script following a MOD instruction. I rebooted and was stuck on boot just after the samsung screen. All my phone would to was give little vibrations every 10 seconds or so.
I was able to boot to recovery, however stock recovery would not fix the boot image.
I have heard of similar problems with booting and thought I would post my fix.
I downloaded a clockworkmod v6 .img file.
I downloaded Odin v3.
I downloaded the S3 usb drivers from samsung website.
I already had a back up made with a previous version of clockwork but I know you can find the stock version of your S3 for download if that is the course you need to take.
NOTE: Odin will not flash .img files. I edited a .tar file with the name clockworkmod.tar and inserted the .img file i downloaded for the S3 into the .tar using Ubuntu on my laptop. If you do not have Ubuntu i know you can find the .tar of clockwork but i just got tired of searching for it. The .img file has to be named recovery.img inside the .tar in order for odin to flash it. I found that out the hard way getting multiple errors.
Using windows XP on another computer (Odin wouldn't flash using VirtualBox inside ubuntu) I first installed the usb drivers for the S3.
Then I started Odin. At the right hand side of the screen you will see PDA. Click that and browse until you find you clockworkmod.tar file and open it.
Uncheck the box at the left of the screen that says Auto REBOOT. if your phone doesn't boot properly (like mine did not) then when Odin reboots your phone you will lose the recovery that you just flashed to the phone. Leave f.reset checked.
Put you phone in download mode by holding down the volume down, power and home keys. When the warning prompt comes up then press volume up to continue. Your phone will will go into download mode.
Connect your phone to the computer and wait for all the windows nonsense about device drivers loading and so on to happen. You should then see that, in Odin, the little rectangle box in the upper right, just underneath the big square box, will turn either blue or yellow depending on your Odin version. Inside the comment box it will also say ADDED! If the box doesn't turn a colour then you need to check that the usb drivers installed properly and repeat the above steps.
Hit Start. It should only take about 10 seconds and then in the comment box it should say RESET OK.
Unplug your phone from computer and remove the battery... Replace the battery. DONT LET IT TRY TO BOOT YET! Mine tried to boot and I had to pull the battery out real fast twice before it finally just black screened.
Enter recovery by holding the volume up, power and home keys together.
You should now see clockworkmod as your recovery agent. If you get the stock recovery prompt or you don't get a recovery prompt at all have no fear. I had to do the steps three times before I got it down perfectly and was able to boot into clocworkmod.
Use clockworkmod to format your sd card. (obviously back up any data that you want to keep off it first) volume keys navigate up and down and the power key is the execute button. Navigate to mount/storage and select. Format is at the bottom of the next screen. There are many tutorials on how to navigate clocworkmod.
Pull out the battery after you have formatted. Pull out the sd card and pop it ino your computer. Place the backup that you have downloaded or had stored on the sd card.
Again, I had multiple backups already but you can find stock .img files out there.
Replace the sd card and boot back into recovery mode. Again, if you miss recovery mode and your phone starts to boot then you will most likely have to start over in Odin to re flash clockworkmod.
In recovery mode scroll down to restore from ext sd card. If the backup file is good you should then see it. Click on the file... Click on Yes. Hopefully in about 3 minutes it will finish and say SUCCESS!
Reboot. If your backup was good you should be all set.
I really hope this helps you.