Try directly with sn0wbreese, that should preserve the BB as well.
I more thing, did you install ultrasnow fixer as well?
I am really sorry, but being a beginner, I tryed in redsn0w to click on extras and then verify and this is the result... maybe this can help to downgrade?!
Nope, this doesn't work too...Ultrasn0w fixer is also for 05.13.04, try that first:
http://www.beijingiphonerepair.com/...ith-ultrasn0w-fixer-patch-old-basebands-only/
So uninstall ultrasn0w, install the fixer then install ultrasn0w again.
If it doesn't work you can downgrade to 5.1.1 with redsn0w
In that case you can skip the 6.0 step and go to extras/even more/restore with a downloaded 5.1.1 ipsw, remote blobs and preserve the BB, after that you can jailbreak with redsn0w and install ultrasnow again
Ok go for 5.1.1
Sn0nbreeze and redsn0w should let you upgrade without uodating the BB, fir redsn0w you'll need the blobs, Cydia saves them automatically, i guess 6.1.3 is still too fresh, so in the near future it should work like discribed, meanwhile you should have a working phone unless there is a hardware probkem on the phone ofcourse.
Every time you connect to itunes the Apple servers are contacted, if your phone(IMEI) is found on the unlocked list with apple the iphone is activated.
The carrier passes on the imei to apple which puts it on the whitelist.
If it is unlocked you can put in any sim, if that diesnt work jailbreak and install ultrasn0w
In redsn0w you should be able to select activate during the process.
Restart the phone and try again with redsn0w
Don't need the fixer on 5.1.1 ultrasn0w should work fine without it on that firmware
Try to get it unlocked by Ofrance, for now just enjoy the phone
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Itunes backs it up automatically, as cydia has your 5.1.1 blobs you can always rrestore to that