First if you have an external SD card installed I would try removing it and restarting. Corrupted SD cards can cause some very strange behavior.
Next I would try restarting in safe mode.
To turn on Safe Mode, follow these steps:
1. Power the phone off.
2. Once the phone is off and all lights are emitting, press and hold the Power button to turn the S4 back on.
3. When the Galaxy S4 logo appears on the screen, press and hold the Volume Down button.
4. Continue to hold the Volume Down button until the phone completely boots. You will see the words “Safe Mode” appear in the lower left corner of the screen if you performed the steps properly.


Let us know if any of that helps!

PS. Sorry for my English too, and I was born and raised in the states!

 

Here's a reply to the same issue from Verizon's site. It will unfortunately wipe all of your data.
The phone has to be completely powered down to start with. Then you'll need to press and hold the Power button & Volume up key & Home key for quite some time. You'd let go of only the power button when the phone vibrates but keep holding the Volume & Home key until you see the Android logo. Once that little green guy appears, you can let go of all the keys. You'll need to use your volume keys to highlight and power key to select wipe data/factory reset, then Yes -- delete all user data and last but not least to reboot the system now.

If that doesn't work here's a discussion of another fix:
http://forum.xda-developers.com/showthread.php?t=2325911&page=2

 

And the "hold the power button, volume up, and home button, release power at vibrate" didn't get you into recovery?
I'm out of ideas. Perhaps one of the true Galaxy experts will chime in because I'm stumped!
Sorry I couldn't help. I hope somebody else here can.

 

Freaksonme I am having the same issue!! Mine started yesterday if you do figure it out on your own can you let me know what it was please?

To everyone else the only way to get the phone to display anything it to take the battery out and put it back in. Once I do this there are 3 options;

1. If I touch nothing the phone vibrates once then will display samsung galaxy S4 for a few seconds then go blank.

2. Hold the power and volume down button it will display a custom OS warning. It then gives me 2 options volume up to continue or volume down to cancel either option I do I still only have the few seconds before the screen goes back blank.

3. Hold the power and volume up button it will display the samsung logo like normal and also show the little blue letters int he top left corner but like before you only have a few seconds before the screen goes blank.

~~~

I've tried several thing also; SD card or no SD card, computer doesn't recognize it.

 

I am having the same problem too.
Can anyone please help us?