When you turned it off during updating, it hadn't fully updated, so you might not have the charging firmware in the phone. Power it with the original charger and the original cable. If you still can't get it to turn on, it's time for a trip to Samsung. If you're in the US, the easiest way is the Samsung Experience Center at a Best Buy store.
If it turns on, download Odin and the latest firmware for your particular model, country and carrier from
SamMobile Firmwares (It doesn't have to be 4.4.2 - even if you load an earlier version into the phone it'll update over the air.) Use Odin to update the phone. (If the line with the firmware ends in an orange box with a K, that firmware can be uploaded using kies. In either case, you'll need some way to power the phone at the same time you have the data lines connected to the computer.