Check this link out. In a short, your corolla has engine problem, like mine. Toyota is aware of it and sent out this bulletin a long time ago. I don't know why dealers have no clue and keep us running around. I finally found and printed out this bulletin and took to the dealer. Good luck.
I finally got my problem fixed. I printed this off and brought it to the dealer service department. They told me the noise was caused by lack of oil. Got the oil changed and next day the noise was still happening.
So I took my MD recorder and I recorded the noise on two consecutive morning starts, brought it to the dealer, asked for a mechanic to listen, which he did. He just said "Well, we will check it out and see if we find anything" I get a call about 30 minutes later saying they would replace the camshaft timing device (described in the pdf file). Two days later, my car is finally fixed. I guess all this time they didn't feel like spending 10 hours on a job covered by power train warranty.