,i've encounter thid problem before with the new macbook not a1181 model...i replace the whole LCD/screen with new LCD which i order here at iFixit... but unluckily it does not solve the problem. the problem is the "onboard video chipset controller". try to reflow the video chips.
,FOUND AND SOLVE THE PROBLEM... one of the memory chips is defective which cause the MAC not to continue boot-up... basically flashing question mark on startup usually cause by crashed HDD and OS but this time i found out that one of the memory chips is malfunctioning......
if the first led lights ON with GREEN, meaning the power supply(PS) is good, when turning the switch ON, second LED must lit... if its not light it means that the logic board is not receiving any voltages at all, check your SWITCH and the swicth connector to logic board, check also the connection of the PS going to logic board.