(FIX) Can't boot into rom, recovery, or download/constant restarts
This is a possible fix for anyone who is experiencing all of the following issues. If you are NOT experiencing all of these issues then my fix is most likely not the cause of your problem.
1) Can't boot into ROM (phone will get no farther than GALAXY S III logo)
2) Can't boot into RECOVERY (phone will try to boot into recovery but will never make it)
3) Can't boot into DOWNLOAD (you may get as far as the caution screen but phone will turn off)
4) Phone starts, then turns off after about 3 seconds.
The solution that worked for me involves the power switch. It turns out that the reason you are unable to boot is because your power button is constantly being pressed due to a "sticky" button. This is a hardware flaw with only a temporary solution.
Steps to FIX issue.
1. Use fingernail to gently remove POWER BUTTON from phone. Notice that the bumps in the middle of the button are a little off-center.
2. Use a pair of fine tip tweezers to gently PULL on the yellowish/white POWER SWITCH inside the phone.
3. Test the fix by reinserting the battery. If the phone doesn't auto boot then press the POWER SWITCH with the end of your tweezers.
4A. If phone continues to power cycle then return to step 2.
4B. If phone properly boots then reinsert the POWER BUTTON with bumps in the middle aligned with the POWER SWITCH. If you don't align the bumps then the button will not function properly.
Once again, if this fix did not work for you then your problem is most likely in software (bootloader) and not hardware.
Hope this helps someone. Cheers!