Describe your samsung syncmaster 204bw Problem: I turn the monitor on, the power button turns blue, the screen remains dark, the image on my Powerbook G4 appears flashes on the screen before it goes black again and the power button is not longer lit it. Then it powers on again and the process repeats. I have unplugged all cords and plugged them back in - the problem remains. Thank you!

Check the power supply DC filter cpas first.
If you are going to DIY and have proper tools and know safety precaution then please read on:
Most common failures in the LCD monitors are bad capacitors (bulging top/seal or leaking) in the power supply (they should be replaced in a set), blown fuses; poor solder joints, failed inverter circuits (blown fuse, shorted transistors, shorted/open transformers), bad lamps (poor solder connections or worn out lamps). You will need to open it up and inspect the inside, see example of failed SAMSUNG monitors to get some ideas what to look for: http://s807.photobucket.com/home/budm/allalbums
Post back what you see inside so we can guide you further and it will help out other people in the future also.

Basic LCD monitor troubleshooting guide:
http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting

Learn about bad caps: http://en.wikipedia.org/wiki/Capacitor_plague

Capacitors kit: http://lcdalternatives.auctivacommerce.com/ he can make you a set of caps for you.