q-tip would be fine. just make sure you are in contact with something that is grounded, and ground yourself before touching the processor to avoid any static problems.
ok, so let me get this figured out.
what model is the X2? (i.e. 4600, 5200, etc.)
what model is the motherboard?
where all did you put thermal paste?
how much and of what brand did you use?
how did you apply the paste? (did you just put a dab, or did you physically spread it out.)
did the computer EVER post?
if the computer didnt post at all the first time that means there is something else going on. if the processor is overheating the computer will come on but will shut itself down to protect the processor from overheating and melting itself. most likely you wont be able to see any physical damage on the outside of the processor, if anything was fried that'd be on the inside...