When I was soldering my CT6B 's  battery compartment (without opening its back cover) so that I can use a 3S lipo, accidentally the positive (red)wire shorted to the negative terminal on the PCB.Since then, my elevator channel (ch2) and aileron channel (ch4) are not working. Any solution for this?

Open the tx and look near the pots of those 2 channels. There may be some problem with the connection near to the pots.
I dont understand from your pics. I do have similar tx but i dont understand whether battery positive got shorted to pcb or negative of battery got shorted.

Ok. Let me try that. Thanks. I'll mark the site where this happened and post a screenshot.

Unscrew the ts and double check every thing , strange to hear that only two channels are not working ,  may be problem with the pot

It was here (arrow in the attached pic) that accidentally   shorted.. Help

The centre pin is signal pin of the pot. Remove the shorted end and try it. I think it would solve the issue. But I feel something else would have happened because if only one pot got shorted then its weird to know that 2 channels are not working. Observe clearly whether other pot end terminals on PCB board is correct. If you have a multimeter check whether the pots are getting supply.
After that check whether signal wire is connected to PCB by doing continuity test from pot signal to PCB.

Okay. Thanks. Let me try that.

Desoldering the shorted area doesn't help All the pot ends are getting supply , but there is a difference in voltage on either side. Is that normal? And yes the connections to pcb are alright. Does that mean the ic is damaged?

Since it's a pot there will be voltage difference on either side ,  well i guess that you soldered the 3s to the pot  from the pics above . If so there's a  chance for  damaged IC The whole circuit works at 5v  and what you connected was about 12 v

Oh my bad. What I do is a mix, so that elev is channel 5 on VR(B). Now I have to train my hands for that.

If you have accidentally soldered 12v terminal to pot then its all over. But you say there is only problem with 2 channels which are good signs of working but you need to figure it how. I think you have mixed up all the terminals.
If your auxiliary knobs working fine and show on t6config then you can replace their signal wires with your pots of aileron and elevator.This time make sure that your pots are supplied with not more than 5v. Check the voltage with multimeter before you switch on the supply. Theoretically  If it works but you will have only 4 channels and remaining two are not usable.
If it works this way  them there might be some problem with 2 channels on the IC.You might have damaged only 2 channels by over voltage.

Let me try that too. Presently I need only one more (elev) ch as I make 3ch planes usually. The Tx's knobs are working perfectly, so as you told, if it works , oh , I am more than happy!

There are better software for the transmitter , try one of them (40% chance ) .  When compared to t6config they are better and more user friendly

The Pot control pins goes through tiny resistors, the resistors have different values to suit its alignment, calibration, if the resistors are burnt or open while using 12v batt, ask Reddy Sir to give values of those resistors, now these pins are directly linked to Control IC, if your resistors are Okay, then change IC, you will get it, online, or www.icchipset.com, My submission to your query is that IC is faulty, as resisters do have good tolerance, and if burnt it is visible, Reddy Sir can take Ohms test of that IC to confirm if its faulty, wish you best of luck

Wow! This is my perfect day! @BalakrishnaReddy, your advice worked like charm!   Now my ele channel is working perfectly! Thanks a lot @BalakrishnaReddy, @a3ruz,@stadsocare   I soldered the ch5 (VRB) wires to ch2 pot.   One of the many reasons why I like this forum!

Calibrate the channels sir ,  use any alternatives software for the T6config ,

Yes ,calibrated using t6 config. Which is the other software? Any link?

Digital radio

www.sgr.info/usbradio/download.htm

Thanks @VOD..

6000 worth electronics ( Tx + 3 Rx) & happiness restored!

Sunil sir keep an eye on the sales thread , you can get replacement board / spare of the same tx ,
Last week Sathya sir sold one CT6B for 200/- ( i guess so  )

Oh.. Okay. .. Sure. Thanks..