I believe this example is flawed. We would never use it in the second sense implied in the thread. The primary reason is that it invites ambiguity. The translated sentence completely misses the "purpose" of "için" (pun intended) in the sentence, while it does correctly identifies the correct object of "waited". This is possibly better rendered as,
"The baby waited for you in order to talk (with you)"
addendum : Sorry I see that Lambdakneit already made this point.
Im confused a bit. to talk basically mean a conversation that a baby expected right? If he was mute until this person came wouldn't it be beter to use the verb to SAY here? Otherwise it is difficult to catch the meaning. Whether he wanted to have a conversation and waited for this person or as i said He pronounced his first words when this person came.