First off you should flash another version of the firmware on your phone just to double-check.
Try 4.2.2 and other versions of 4.4.2. If it doesn't work then try some of the custom firmwares like CarbonROM and others.
If it still doesn't work then your sim card reader is defective and needs to be replaced.
You can buy it from eBay (search for "S4 active sim tray") and order ascending by price. It costs about $6.2 without shipping.
It is fairly easy to replace, just pop a few screws out the back and it is the first little board that you see, disconnect the flex cable, take it out and put in the new board.
Alternatively if you cannot buy from ebay from various reasons, go to your local GSM repair shop and ask them to replace just the tray, it is compatible with multiple phones and it is replaceable by Hot Air rework.