we wonders, precious, we wonders *gollum*

[Imladris]

No, he made the noise soon after he discovered the Ring:

He took to thieving, and going about muttering to himself, and gurgling in his throat. So they [his relations] called him Gollum , and cursed him, and told him to go far away;

Maybe he forgot how to laugh. The book says that he would eavesdrop on secrets and use his knowledge for wicked ends. Maybe he laughed in spite, but as time went on and he became so miserable, all that came out was a strangled sort of sound: Gollum. Now, if that's the case (which is doubtful but that's the first thought that came to me), it wouldn't sound like the movie version of Smeagol's gollum. I'm going on the fact that he "gurgled in his throat."

Or maybe he had a severe case of post-nasel drip he never got rid of.