Stock SGH i337 - Won't Power On topic

I'm not a complete n00b, but this phone has never been rooted. Was working normally and it powered down at complete random. When I reinsert the battery, it powers up for about 2 seconds. Shows the logo, vibrates, and shuts off. Dead as a door-nail. It doesn't appear to begin booting, When entering safe mode or recovery mode it does the same exact thing. If the phone is plugged in, it shows no signs of life. No charging light, no logo screen or vibration. Nothing at all. I'm out of warranty.

Guys, if there's anything I should do before buying a new phone, please tell me. because I am lost.