Macbook Black (late 2006) MAJOR PROBLEMS

So we'll through this as succinctly as possible I bought my black macbook in 2006 after my beloved ibook g4 failed (don't start me on that one) the blackbook was fine for the first three weeks or so before the fans stated going berzerk. about three months ago the hard drive failed and apple replaced it Yesterday I put the computer to sleep when I woke it again it shut down as it as been want to do for the last several month (Rapid shut down syndrome) when I restarted it it did not boot when I turn it on it loads to a blank white screen no question mark nothing just a white screen which to me indicates that the screen is toast but I am probably wrong. is there anything I can do my self or am I going to have to take it in for the millionth time? and if so would it be worth it to just buy a new computer?

thanks in advance,