It seems that Kovalainen did not have brake problems at the start of the China GP (other than the smoking brakes on the grid but this was the surrounding carbon fibre getting hot which was then cooled once he got going) but massive understeer. This contributed to him losing the place to Alonso on the first lap when he had to lift going through turn 13.
The understeer was caused by a team mistake. The front tires had been mismatched and the front right was on the left and vice versa. It would appear that the front tires are identical, but the problem was caused by the construction of the tire. The Bridgestone tires are a crossply / radial hybrid and there is a difference in the stiffness across the tire to give an artifical toe-in effect for better turn in and mounting them on the wrongside has the stiffness working in the opposite direction, thus inducing understeer.
McLaren compound the problem by not noticing this problem at the first pit stop and dialing in extra front wing for a problem that was no longer there and gave him a dose of oversteer for his second stint.