Volume Down+Home+Power. When you get the warning, go to download mode, don't reboot.
Use
Odin and a copy of your phone's ROM from
SamMobile Firmwares (enter the model number, not S4) to reflash.
If you can't even get to download mode, look on ebay for Samsung Download Dongle. The 88 cent ones are the same as the $4 ones, so buy the cheap one. Short instructions - remove the battery, plug the dongle into the microUSB connector and replace the battery. If it doesn't power up, press the power button.
If it's still dead, take it to a repair shop - it may need hardware replaced.