I registered literally JUST to make this reply.
I purchased my S4 Active (AT&T) after my iPhone 5 dropped resulting in a broken screen. I've used iPhones since they were released, am an app developer, have an Apple TV, Retina Macbook, my fifth Macbook Pro (started with a Powerbook G4), and lots more. You could say I'm an Apple fan, but I wanted to try something new and was sick of how restrictive iOS was without a jailbreak.
I loved the phone for a week and then started to regret my decision.
Long story short, I've had the same problems as all of you. Tonight, I've been playing with my phone for literally 4 hours while stuck at the startup screen with the empty battery showing, and a frozen progress indicator (a circle that looks like it would rotate, but is frozen still). Unplugging and starting it up shows the Galaxy S4 Active splash screen for about 3 seconds and then it dies. If I plug it in while the splash screen is shown, it just stays frozen there. If I turn it on while plugged in but with no battery, the screens backlight just flickers on and off.
I tried two cables, factory and aftermarket. Two USB ports on my laptop and desktop, two wall chargers, literally every combination you can think of.
Somebody replied here saying they charged it in their car and it fixed it - DING DING DING! I ran out to my car and plugged it in and got the same battery screen with the frozen circle and was very upset... but two seconds later the screen turned off, and then came back on with the normal battery with a green charge indicator inside of it! Hooray! I let it sit in the car for about 15 minutes, and then ran inside and plugged it into the wall (while leaving it off the entire time). It did boot up to the frozen screen, with the empty battery and frozen circle, but I let it sit and about 15 seconds later is turned off and back on to the charging screen.
I dont know why DC vs AC would be an issue, and I used the same cable in the car that I tried inside, but it IS a fix and has worked 100% of the time for me so far.
I've had nothing but issues, my battery dying extremely fast even with power saver on and with my CONSTANTLY killing all processes and lowering screen brightness. While charging in the car, if I'm playing video or using maps the battery actually DEPLETES while on the charger! It charges SO SLOWLY that I LOSE battery with it plugged in. Regardless of whatever argument about wall chargers vs usb charging, that should not be the case. My iPhone 5 charged in half an hour WHILE being used on the same car adapter, and while demanding much more out of the phone at maximum brightness and while streaming HD video.
The phone has serious hardware and/or software issues. It's running much slower and is just a pain in the ***. I will not be satisfied with Samsung unless they COMPLETELY replace my phone at this point. The fact that I paid almost 800 dollars outright for this infuriates me.
tl;dr version: If you cant charge your phone and it's stuck at the screen with an empty battery and a loading "circle" icon that appears to be frozen, go plug it in in your car! Let it sit for a bit and the charging screen will come up; if it doesnt, force shut it down (hold power button until the screen goes black). This was literally the ONLY THING THAT WORKED for me, and I tried absolutely EVERY possible alternative. Good luck, guys!