Does this sound natural? If not, please correct it.
In hearing-impaired babies, there is a type of babbling thought to signal an emerging capacity for speech is distorted.

It's fine until the last two words - then it all goes wrong. 

How does 'is distorted' relate to the rest of the sentence? You might need to try rewording this to make it clearer.

Su.Ki. is correct in her comments...maybe this is what you intended, Shao?:

"In hearing-impaired babies, there is a type of distorted babbling thought to signal an emerging capacity for speech."