Accessing heatsink on Vaio PCG-FRV31

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My Vaio PCG-FRV31 has been heating up and shutting down. I've opened
it up and removed some of the dust in the fans, which seems to have
helped, but I want to get access to the heatsink to clean it off and
add new thermal compound.

I've got the keyboard off and the metal plate underneath, but when I
unscrew the four screws around the main fan, nothing seems to happen
-- it still seems stuck onto the board.

Any suggestions?

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