[Galaxy Tab 4 General] :
I managed to pull some files together including the .pit file from my now working tablet and make a fully working 4 file firmware and combo (all in one) firmware that CAN be flashed with Odin. I have tested it on my device and it does work. Since I know people are searching EVERYWHERE for this, I have released a download link for these files below.

Please, feel free to re-post this anywhere, just be sure to credit me.

DISCLAIMER (Obviously): I WILL NOT BE HELD RESPONSIBLE FOR ANY DAMAGE DONE TO YOUR DEVICE AFTER FLASHING. KEEP IN MIND THAT ANYTHING CAN GO WRONG, EVEN IF YOU'RE FLASHING FIRMWARE THAT IS MADE FOR YOUR DEVICE. THE FIRMWARE AVAILABLE BELOW HAS NOT BEEN MODIFIED, ENGINEERED, OR EDITED IN ANY WAY TO CHANGE THE FUNCTIONALITY OF YOUR DEVICE. IF YOUR DEVICE BRICKS AFTER FLASHING, IT'S ALL ON YOU.

Flashing instructions:

But first, the requirements:

1) SM-T337A, Obviously, but seriously, I can't stress how important it is that you check that your model number is matched with the model number in this thread before flashing anything.

2) A Windows pc (NOT A VIRTUAL MACHINE! Using a VM to flash your device has a high chance to hard-brick your tab, and make sure your computer is running Windows XP or newer.)

3) Your device's USB transfer/charging cable

4) A Brain (Obviously)

Now then, the actual steps (4 File Firmware):

1) Boot your tab into download mode (Shut the device down completely, then hold down the power, volume down, and home button at the same time until a warning message appears)

2) Download and open Odin on your pc

3) Grab the USB charging cable and plug your tab into your pc

4) If Odin does not show your device in the list (It will display an "Added" message if the device is detected) download the Samsung USB Drivers for Mobile Phones and install it to your pc. You may need to/and it is recommended to restart your computer after installing the drivers.

5) Extract the zip file you downloaded containing the firmware to your desktop or a memorable place on your computer.

6) If you wish to wipe your data and start from scratch, click on the 'PIT' tab and select the .pit file in the extracted folder. Then, click the 'OPTIONS' tab and select 'Re-Partition' and 'NAND Erase All'.

7) Insert the firmware files into Odin. Within Odin, for instance, Click on the 'BL' button, which is where the bootloader file goes. Select the extracted package that has 'BL' at the beginning, and vice versa.

Example:

BL: *directory*/BL_T337AUCU2BOH4...

AP: *directory*/AP_T337AUCU2BOH4...

CP: *directory*/CP_T337AUCU2BOH4...

CSC: *directory*/CSC_ ATT_T337AUCU2BOH4...

8) Once done, verify that you have correctly done all the steps above, click 'Start' in Odin and wait for Odin to output a "PASS" message before unplugging anything.

9) If you wish to flash the firmware, but keep your data, make sure that there is no .pit file in Odin, make sure that 'Re-Partition' and 'NAND Erase All' are unchecked, and make sure that there is no file inserted under the 'CSC' row.

Tutorial (Combo Firmware)

1) Boot your tab into download mode (Shut the device down completely, then hold down the power, volume down, and home button at the same time until a warning message appears)

2) Download and open Odin on your pc

3) Grab the USB charging cable and plug your tab into your pc

4) If Odin does not show your device in the list (It will display an "Added" message if the device is detected) download the Samsung USB Drivers for Mobile Phones and install it to your pc. You may need to/and it is recommended to restart your computer after installing the drivers.

5) Extract the zip file you downloaded containing the firmware to your desktop or a memorable place on your computer.

6) Within Odin, Select 'AP' and browse to the directory where you extracted the firmware, and select the .tar package in the directory. There should be nothing else under the other tabs, only 'AP' should have a firmware package in it.

7) Flashing this package (unless you perform the "Developers Tip" at the end of this thread) will wipe all of your data, so be sure that the proper .pit file that came with the firmware package is selected under the 'PIT' tab in Odin and make sure that 'Re-Partition' and 'NAND Erase All' are checked in Odin to ensure a complete wipe of all personal data on the device. If you perform the developers tip at the end of the thread, simply insert the new package you created under 'AP', make sure there is no .pit file under the PIT slot, and make sure that 'Re-Partition' and 'NAND Erase All' are unchecked in Odin.

8) Once done, verify that everything is set and ready-to-go, then click 'Start' and wait for Odin to output a "PASS" message before unplugging anything.

9) Enjoy!

WARNING: If you are seeing sites that charge you money for the files, DO NOT BUY IT. They are scams and I HIGHLY SUGGEST AVOIDING THESE SITES. I didn't have to buy anything. If you do buy the firmware from these scam sites, and your device becomes bricked or messed up in some way, don't say I didn't warn you.

4 File Firmware Download: https://mega.nz/#!n8Q3VIIS!OComhygeI5SL5R6n0EXEfiYMBtVn_aOAIcUuLgmYs-k

Combo Firmware Download: https://mega.nz/#!69oEwbBR!vBtHQnrdwAfdZB3iPeGb99Yp7W79efTQr7t6FZXrzIo

Odin 3.12 Download: https://mega.nz/#!KsZiHKTb!aEHdQgO7JAQeUwdJWqS0xoR3lyJH4ieJ6qTbVKce8Zk

If the link doesn't work or goes down for some reason or if you were confused by my instructions in any way, please let me know.

Developers Tip: If you want to flash firmware without wiping your data, make sure there is no pit file selected under the PIT tab in Odin, then extract your firmware package (extract everything into a separate folder for combo firmware, extract the CSC package for 4 file downloads) and remove cache.img.ext4 then repack as a .tar file. Applies to both combo and 4 file firmware packages. In 4 file packages, cache.img.ext4 is in the CSC file. However, in some cases this may put your device in a bootloop. If you wish to do this on an older device and the cache file doesn't have the .ext4 extension at the end, don't worry, it'll work the same way.

Now that you have the firmware, WHY NOT ROOT IT? Check out my thread on how to do so here: https://xdaforums.com/tab-4/general/root-how-to-root-sm-t337a-supersu-t3553848

Cheers! :D