Your baby can talk - you just have to learn their language until they learn to talk in yours.  This pediatrician article says it's a lose-lose situation for parents and babies if not responding to a cry and just ignoring it:

By not responding to the cry, babies and parents lose. Here’s why:

In the early months of life, babies cannot verbalize their needs. To fill in the gap until the child is able to “speak our language,” babies have a unique language called “crying.” Baby senses a need, such as hunger for food or the need to be comforted when upset, and this need triggers a sound we call a cry. Baby does not ponder in his little mind, “It’s 3:00 a.m. and I think I’ll wake up mommy for a little snack.”

No! That faulty reasoning is placing an adult interpretation on a tiny infant. Also, babies do not have the mental acuity to figure out why a parent would respond to their cries at three in the afternoon, but not at three in the morning. The newborn who cries is saying: “I need something; something is not right here. Please make it right.”
(via "Let Baby Cry It Out: Yes or No?" on askdrsears.com)

Do you really want your baby to learn not to communicate that something is wrong? Or to let you know when something is wrong?

The cry is a marvelous design. Consider what might happen if the infant didn’t cry. He’s hungry, but doesn’t awaken (“He sleeps through the night,” brags the parent of a sleep-trained baby). He hurts, but doesn’t let anyone know. The result of this lack of communication is known, ultimately, as “failure to thrive.” “Thriving” means not only getting bigger, but growing to your full potential emotionally, physically, and intellectually.

In summary: "Parent Tip: Babies cry to communicate – not manipulate."

Since the cry is a baby’s language, a communication tool, a baby has two choices if no one listens. Either he can cry louder, harder, and produce a more disturbing signal or he can clam up and become a “good baby” (meaning “quiet”). If no one listens, he will become a very discouraged baby. He’ll learn the one thing you don’t want him to: that he can’t communicate.

What Can Happen

Baby loses trust in the signal value of his cry – and perhaps baby also loses trust in the responsiveness of his caregivers. Not only does something vital go “out” of baby, an important ingredient in the parent- child relationship goes “out” of parents: sensitivity. When you respond intuitively to your infant’s needs, as you practice this cue-response listening skill hundreds of times in the early months, baby learns to cue better (the cries take on a less disturbing and more communicative quality as baby learns to “talk better”).

Read the full article "Let Baby Cry It Out: Yes or No?" on askdrsears.com