Why didn't you read CM 10.2 thread? It is written that it has black screen on recovery.
Originally Posted by Cocutzul
Try with Odin again, try to pull and put back usb cable. You have Windows 7? Does it show new hardware at all?
You have used Odin before? If not look for some guide on youtube. Maybe you miss something.
Try with ODIN v1.85 and ODIN v3.xx
Do you have any PC activity when you get to Recovery? I read that it just has black screen, but it is functional. Maybe ADB shell is working, so you can flash CoCore over it.
You can try to install this on PC: http://forum.xda-developers.com/show....php?t=2105707
There you have adb shell, and with some commands you can install kernel. After that you can reboot to Recovery again and you will have working Recovery (but still non booting system). Next step is to download some JB stock based ROM and to push it to sd card (you can use that Total commnader in link I gave you). After that just install ROM and it should work.
I am at work now, so I can't help you in details.
If I helped you, be kind and hit Thanks button.