Devo 8s Found a resistor BURN

That is the power resistor. it is tied to a couple diodes and then a 3.3V regulator. My guess is that at 7.4V you are putting about 3 times as much power through that resistor as it was designed for.
It is a 10 ohm half-watt resistor. for a 7.4V supply I'd probably replace it with a 20ohm 1watt resistor (but you'll probably be stuck with Lipos going forward since that would significantly raise the minimum voltage required to run the Tx). You could also use a 10ohm 2 watt resistor if you want to be able to go back to a 4.8V pack, but you'll be wasting a lot of power as heat.

Actually mine is a 6.8Ohm as well. I just read what was on the silkscreen (10ohm) and assumed they'd followed it.
The power circuit is a bit odd. I have a full diagram of it somewhere. I think there is something wrong with it as I smoked one of the switching transistors doing nothing more than turning the Tx on/off (the cheap switch failed which somehow led to the transistor burnout). It is also possible that the resistor does get really hot due to the Lipos, but hasn't failed. Did you check it with an ohm-meter (with the batteries removed of course)?
the full voltage also goes directly to the CYRF Module which has its own ldo. Rereading your 1st post it isn't clear if you are having a range issue or if the tx is no longer functional. If it is only a range issue, you probably burnt out the cyrf power-amp. The only way to know is to remove the shield and check it.

you'll probably be better off to just buy a new module for $10. fixing the CYRF module will be rather challenging unless you have access to the micro-smt devices or PA parts, and the ability to do fine-pitch qfn soldering.

I don't have a circuit for it, but you can find a documented image here:
openrcforums.com/forum/download/file.php?id=538

Link page is here:
openrcforums.com/forum/viewtopic.php?f=5&t=362