[Verizon Samsung Galaxy S III] Droidriven:
The ROMs were actually built for the Verizon S3(SCH-I535), they are 4G devices, this makes them require a SIM card to regulate the 4G data they use, this makes our device require a CDMA LTE SIM(Verizon 4G LTE SIM or Straight Talk CDMA LTE SIM from the BYOP kit, the LTE version, not the GSM AT&T/T-Mobile kit). I'm actually the one that figured out that a SIM was needed for the ROMs to work. I can explain in detail, but I'll keep it short instead.

Even though our device is 3G and doesn't require a SIM under normal circumstances, with the SIM inserted in our device with those ROMs, we then have working mobile data and MMS, sometimes it requires setting APNs in the ROM along with using the SIM to get stock MMS working, otherwise, MMS would only work when using a 3RD party app for MMS.

A lot of people bricked this device trying to figure out why mobile data wasn't working before I discovered this SIM dependency. I've actually worked with a few developers trying to remove the SIM dependency so our device could use the ROMs without a SIM but nothing works, anything done to remove the dependency, kills all chances of connectivity, even call and text. I also helped with creating the first and only TWRP custom recovery specifically compiled for our d2tfnvzw(Tracfone on Verizon network Straight Talk S3) device. The other recoveries are actually d2vzw(Verizon Wireless S3) but they work on our device also, just not specifically.

The Straight Talk S3 can use the Verizon recoveries and ROMs because it is actually a rebranded Verizon S3(SCH-I535) and actually has the I535 model number stamped on our motherboards and other hardware inside our device, the only difference is that the 4G capability was disabled in the radio(no, using the 4G SIM will not give you 4G data). It is not "similar" to the Verizon S3, it IS the Verizon S3 modified for Straight Talk.

I can actually get you set up with some very good 5.1.1 Lollipop custom ROMs packed with features including working camera(we have marshmallow but front camera isn't working, that is always an issue with new ROMs because stock camera is closed source software, developers are not allowed to use it, they have to piece the coding together from scratch so it takes a while to fix), if you can get a used, previously activated Verizon 4G SIM($3-5 on eBay, used SIMs are better than new SIMs, new SIM gives aggravating issues) or Straight Talk BYOP LTE SIM. The ROMs are MUCH better than the stock JB 4.1.2 firmware. Let me know and I can get you setup and you won't even need the PC to do any of it. It can all be done with apps and your mobile browser. Using WiFi to download on the device instead of mobile data to download the ROM files you'll need, the apps that will flash the files you need are very simple to use. After the files are downloaded all you need is a click here and a click there and about 30 minutes of time and you'll be running something much better than stock with everything working as it should.

I have a guide posted here for flashing CM/CM based ROMs on our device and how to set up SIM and APNs, along with precautionary steps for your protection and troubleshooting steps for data issues after flashing the ROM and how to restore data connectivity if you do something wrong along the way.

If you do a google search using our model number, you'll find stuff everywhere that I have posted about this model number.