It is weared that after a factory reset you lost your IMEI. this is written in the efs partition in the root of your phone and usually gets lost if u flash custom roms.
Have u unrooted your phone and install any rom right after that factory reset?
If u r rooted, install x-plorer and look if u have any backup of your efs folder. There are some methods to restore and first save your efs partition. That is the the place where your IMEI, ip, serial no, Bluetooth and wireless no. are written. Without this u can not use your phone with your network.
I had the similar problem with my s3 and very hardly restored my IMEI. On xda are a lot of methods about this, and on other forums. For me it took 2 weeks of searching and I finally did it with a method but at least I had a efs partition saved. There are methods how to do it if u do not have efs saved but not all will work.
Try this steps:
1.If u never rooted your phone u might go back to the shop for repair.
2.if u are rooted u can flash back the stock rom, stock recovery, use Triangle Away that u can find for free on xda to reset the counter of your device to 0 so u get back your warrantee and bring it back to repair.
3.if u want to try for your own just search on xda and in Internet(youtube) about restoring imei.
4.There is a guy from Poland that can restore it through team viewer for 10 euros,if your model do not require a special cable. U can find him on xda or I might give u link but I am not home yet.
5.there is a program to install on your Windows that allows you to rewrite your IMEI in the phone but if u write another imei is illegal. I could not do it just bcs my windows 7 do not recognize the ports in device manager so neither the program could not see the phone connected even if in my computer I could see it.
6.u may try to go to a normal repairing shop to restore imei. They have that cable and a small electronic device and with a click they restore it. In Bruxelles cost me 45euros but in London and US they say is about 10-20 DOLLARS or Pounds.
I wrote u a lot but let me know in which stage u r.
Sent from my GT-I9300 using xda app-developers app