Well i've got a similar problem.
Waterdamaged iPhone (2nd waterdamage on the phone within a few weeks)
Cleaned it up with some Isopropanol and it worked fine (it even had a burn mark(you can even feel it) on the back of the logic board where the "heat sticker" is located)
So after the 2nd waterdamage it looked way more injured (lots of verdigris and some corrosive solder points on the connectors)
Well after the whole cleaning stuff i've put it back together but it's dead...
No recovery, no DFU, nothing!
All that happens is if i charge the phone it gets really warm within a few min (exactly the battery) and i think that the place around the baseband chip heats up too so i have no clue what i can do...
It's 100% the logic board i've tested everything else.
I have a solution!
Tnx to this site i solved my problem.I am writting it step by step.
my iphone wasn;t recognized by any comp. .had black screen, wasn't charging, wasn't recognized by itunes
I did this: i connected iphone not to the charger but to small stand that i got with iphone. My device was recognized like Ipad.I used blackra1n and put it into recovery mode. Then i restored it to original firmware. after that i used balckra1n again and Jailbraked it. I was doing all these things on windows 7.
Let me know if u solved it like this, my iphone was completely dead but this helped.