If you think it's gonna take too much to do it, just feel free to look for another way to fix your problem, but the way I did it, I didn't have any problems, so it's your decision whether to do it or not.
So let's start:
Charge your battery before this. Use TriangleAway to reset the flashcounter, in case it's increased.
PART 1 (downgrade to GB) (Optional- you could skip to Part 2, but if the problem is still there, then it means the "modemfs" file will work only with this version of GB I uploaded bellow):
1. You have to downgrade to GingerBread, so download this: I8160XXLK6 and extract it.
2. Download Odin: Odin3_v1.83.zip Install your drivers as well, if you don't have them.
3. Turn on USB Debugging mode from "Developer options"
4. Enter "download mode" by long pressing vol down + home + power, then press volume up again when you see the warning screen.
5. Open Odin as admin
6. Connect your phone through the usb cable and wait till the ID:COM section turns yellow.
7. Click on PDA and choose "CODE_GT-I8160XXLK6_CL1211243_REV00_SEC_KEY_LK6_4G.tar.md5" from the extracted archive. For I8160P download this :CODE_GT-I8160P_I8160PXXLK2_CL1211774_REV00_user_SEC_KEY_XL K2_4G and put it at PDA after you extract it.
Click on CSC and choose "CSC_GT-I8160-MULTI-CSC-0XELF1_SEC_KEY_4G.tar.md5". Then click on PIT and choose “GT-I8160_EUR_XX_4G.pit”.
“Re-Partition”, “Auto-Reboot” and “F Reset Time” options have to be selected as well. (tick re-partition if you have a 3 files stock GB; don't tick it if you have a one file stock ROM--- these are the rules)
8. Click "Start" and wait till everything is finished.
9. Configure you device, till you get to the main screen.
10. Download flashable supersu update_su.zip and copy it to the external sdcard.
11. Enter recovery mode (vol up + home + power button), and click on "apply update from sdcard" (or something similar) and choose the "update_su" file
12. Reboot and after that, download "Android terminal emulator" from Google Play Store.
PART 2 (repairing the baseband). The "modemfs.img.md5" file was extracted from a GingerBread ROM so I don't know if would work if you tried to put it on a Jelly Bean. That's why I added "Part 1" above:
13. Download this Ace2modemfs.img.md5.zip and extract it.
14. Copy the extracted file ("modemfs.img.md5") to your sdcard (internal)
15. Now open the "Android terminal emulator"
16. Type in what is between the quotes: "su". Click on Grant (Allow, or whatever)
then "dd if=/sdcard/modemfs.img.md5 of=/dev/block/mmcblk0p2".
17. After that, close the terminal and reboot the phone. Go to settings-> about phone and check to see if you still have baseband "XXXX". if you don't, go to recovery mode and make a "wipe data".
After everything is finished use Samsung Kies to update to JellyBean. This way you'll be sure that you get the correct update.
With the exact same steps from above, I managed to fix my baseband. I'm not 100% that it will work for you too, but I'm 95% sure that it will. So follow the steps carefully and you'll be good.
If someone tried only PART 2 and worked on a Jelly Bean, just tell me and I'll delete the first part, which is basically a tutorial for GB downgrade.