Dude, I'm having the SAME problem! Well, not exactly... mine's worse! My 2010 macbook isn't even recognizing that it's even plugged into my 2010 1080p LG 😟 (using the same mini-display to HDMI). Won't detect display, TV says no signal.
I'd all but assume it just came broken in the mail (supposed to be "new"), except that when I connect the macbook and tv (which is connected to some external speakers) at the same time that my computer is connected to the same external speakers (basically the computer is outputting audio twice to one recipient), it buzzes which means the mini-display > hdmi cable is sending some sort of signal... ugh, weird!
I tried every instruction on this thread and on every other thread I've found similar situations. I haven't found another post with the same exact situation as mine.
So ya I'm like incredibly frustrated.