Help with the Heatsink on Precision 360

I was given an old Precision 360 MT by a friend. So I am going to give it to one of my kids. I want to make sure that the CPU thermal paste is fresh and not as old as the computer, but I cannot take of the heatsink. Does anyone either know the trick or have a link I can find it out on? I have tried the clips, but I am afraid if I push any harder I will break them.

Thanks in advance.