I just experienced a similar problem as OP, and I didn't even flash a new ROM or international ROM. Since January, I've been using the ICS version of FreeGS3, stock kernel.
I haven't flashed any new ROM's since January 2013 and have not experienced any problems until now.
This morning, however, when I woke up, I discovered that my Sprint S3 was stuck on the "Samsung Galaxy S III" logo. I pulled the battery and powered up, and it got stuck on the same logo again. I repeated this process several times and the same thing happened. After looking at some XDA threads, I went into recovery and decided to wipe cache and dalvik to see if that fixed anything. Again, the phone booted up and got stuck on the "Samsung Galaxy S III" logo again.
However, when I tried to boot into recovery again, I wasn't able to do so. I tried several times without any luck. I decided to see if I could put the phone into download mode. I did, and it was successful. I didn't do anything just yet because I needed to research more fixes before seeing what needed to be done. I put the phone into download mode several times without doing anything, but then later, the phone itself wouldn't power on.
No matter what combination of buttons I pressed, the phone simply wouldn't power on. I even tried other batteries which I knew were fully charged. When I put the phone on the charger or plug it into my PC, no charging lights light up. However, when I pull the battery an plug the phone into my PC, the charging light lights up and it the PC seems to try to install drivers. However, despite the charging light lighting up with the battery pulled, but phone plugged into the PC, I still can't get the phone to power on at all and therefore can't get into recovery or download mode.
It's similar to the problem the person in this video is having where he uses a jig to get back into download mode.
I have a jig on the way, so hopefully that helps fix my problems, but I don't really understand how the phone got bricked in the first place; First it was soft bricked when it got stuck on the "Samsung Galaxy S III" logo, but I was still able to get into recovery and download mode. Then, it was hard bricked when it wouldn't even power on to get into recovery or download mode. Did it get hard bricked because I went into download mode too many times? What might have caused it to be soft bricked. The thread for my ROM is now closed, so I don't know where else to ask these questions. I'll update you as I try to fix this problem. Any other suggestions are welcome.