I agree with "mayer," just remove the battery and start it up. May I suggest that you go ahead and change out that noisy fan that you were talking about. Ventilation is a MUST for these MacBooks, so resolve that first and then start it up. If the same problem happens again then you might be looking at a logic board replacement but, before we assume that it's that do this procedure here first: Turn on the machine and immediately hold down the Command and S keys together, hold them down until you see the apple symbol with the "spinning" ball. Once you see that, let the keys go and let the machine run it's course. When it finishes (after about 1 minute) type in the following info exactly as you see this: fsck -fy, then press the ENTER button. If the machine is still running then just wait until you see the final results displayed. Now, if the system finds problems with the disk it will automatically fix them and the final message will be something like this: The hard drive appears to be OK.
That is what you want to see, now type the words LOGOUT and press enter. The machine will then restart up on it's own, from there you can take it and see what happens then. Hopefully (if the machine does not shut off during that process) your issues may be resolved. If so, what you will realize is that the hard drive was/is the issue and needs replacing, especially if that test found "Bad Sectors."
Alright I just saw your latest response. Now you're getting some kind of action here, what we are now trying to do is to keep the screen up long enough for it to complete a full cycle of repairs. Try this: when you turn on the computer, hold down the "R" key before it boots up and keep holding it down until you get a screen with the spinning ball, then you can let go. What this is suppose to do is to "Reset" your screen. Let's hope this will help.