I think we have more or less the same problem....
I cannot charge my iphone.
It will only turn on when plugged in.
after plugging in it will only show apple logo for 40 seconds.
Then it will shut down.
During restore It will shut down around 40 seconds too.
the phone cannot reboot by itself.
I TRIED (as meention below)
I bought 2 new batteries to replace. (NOT WORKING)
I tried charging for hours with both new batteries. (NOT WORKING)
I tried restoring original firmware ( IT shuts down after 40 seconds)
Can someone ADVICE on this problem.
THANKS