When TIDO Wave got to Chaui Station site there was nothing there. So assume they came late. They were accused for it. Tagruato is the mining company, but there was no oil at Chuai. The common theory is that they were drilling for either A: Deep Sea Nectar (The not so secret ingredient used in Slusho), or B: Finding the monster for themselves. In a Jamie and Teddy video (
http://www.youtube.com/watch?v=mx73FecqJgk), Teddy says that they've either Found, or are Making something. In the Cloverfield Manga thing it appears there is a boat dragging the creature behind it. You could connect that with the pictures of the dead boat on 1-18-08.com
So let's see. Something falls from space, but I don't think its the monster. What ever it is could have washed out to where Tagruato set up the Chuai station. They go mining for it, but find something else. It attacks, and eventually the military come and knock it out. A Tagruato ship begins dragging it's body behind it. But as we've seen in the movie, explosions don't have much effect on this thing. It kills the ship and starts swimming. Shows up in Manhattan, and the rest was history.
What fell? Was it a Parasite that merged multiple sea creatures (Angler Fish/Snake, Whale, etc.) to create one big monster? Or was it Deep Sea Nectar? Or are the two the same?
I don't know. Hopefully the DVD sheds more light on it.