I have the same exact problem with my LG Rumor Touch. It's absurd! I can hear the person on the other end fine, yet they can't hear me. It has nothing to do with signal strength, because it happens whether I have half of a bar or 4 bars; turning up the volume during the call is not helpful, either. When this first started happening, if it kept being a problem I would turn the phone off, take the battery out for a minute or so, and then put it back in and power on. This seemed to sometimes help, however it is no longer solving the problem. My phone is unusable for calls, and is pretty much reduced to a very expensive instant messaging handheld device. I'm in the process of finding a replacement phone, and unfortunately will probably have to shell out a few hundred bucks for one. Guess I'll be eating Ramen noodles for the next two weeks, eh?
I would appreciate immensely any feedback as to what is possibly causing this to happen and if there is any solution.
EDIT: Just thought I'd give an update - apparently the problem was the microphone(shot). Unfortunately, this is not something that can be fixed by the techs and I ended up having to replace my phone. However, the Sprint store was able to order the replacement for me and swap out my contacts from my old phone to my new one. It was $35 and the best part is, my contract was not changed at all.