Let me guess, go to settings and device / phone info and then look for these values:
Baseband: Probably going to say 'Unknown'
Then head to phone status / status area
Look for IMEI: Probably will say 'Unknown' or 'Null'
If these two occur this is because the modem (It's basically a software firmware device driver that controls the baseband, sim card reader, 3g / 4g cellular signal reception and checks IMEI number.) has gone bad.
To fix this simply reflash the firmware on your phone (Use latest android version and matching carrier (optus for example, also match the CSC code which is a good thing to make sure you are getting correct branded firmware. to avoid issues and factory reset is not required after doing so).
Since it's already factory reset either do it via Samsung Smart Switch / Samsung Kies emergency firmware installation method or flashing it via ODIN using the instructions on how to download and flash samsung firmware onto your phone below:
I had a client come in a few weeks ago with the exact same issue but on a Samsung Galaxy SIII (GT-i9305T). He did a factory reset through settings and it seems to have somehow corrupted the modem firmware during the process.
So I did the steps above to get it working again.
To check CSC type turn the phone off then hold power button and volume up and power for like 15 seconds, make sure to release power button when the samsung logo pops up.
It will say booting recovery mode... in blue text on the top left to tell it is booting recovery mode.
Let it start up recovery mode and wait for menu to show up.
It should say applied Multi-CSC code: xxx <--- The 3 character code is your CSC code that you should match up on the firmware downloader website.
In this image you will get a clearer understanding:
Look at carrier column with the 3 letter combination in brackets, thats the carrier code to assist you in selecting the right carrier and region for firmware.