that white stuf is thermal paste! go to a computer shop, and buy some new past, otherwise you risk frying the CPU. anyway, put a thin layer on to of the cpu again (note: i mean reallt thin

) because that stuff filles up the tiny gaps between the heatsink and the CPU. (bacause its never 100% flat

)
anyway, yes, that white stuff could have been the problem, because its fetting old, it might isolate the CPU from the heatsing instead of connecting them. so probably, your CPU was overheating, because it couldnt get rid of the heat. (because of that old stuff

) and mainly motherboards have a temperature sensor, so ifthe CPU gets to hot, the mobo shut's it down. (and guess what?.. the pc crashes then ^_^ )
anyway, because of booting upo, the CPU is under full stress,.. so i think its quite likely
anyway, get paste like arctic silver 5. thats really good stuff
EDIT: but dont put to much on the CPU, and only on the small square