Humm.. Where to start. I used to have this happen all of the time when I was first building my computers.
First, I do not know your knowledge level, so please do not take offense:
Are you sure that you have the power button hooked up correctly? This sounds strange but I have seen it many times. The green light indicates that the motherboard is getting "stand by" power.
First, lets start with your power supply. There is a very easy way to test it. Unplug it from EVERYTHING on your computer, hard drives, CD-ROMS and all of that. Take the large connector that connects to your motherboard and short out the two pins described below. Just use a small piece of wire or something. This way you can turn on your power supply manually and check its operation.
PLEASE UNPLUG EVERYTHING THAT IT IS PLUGED INTO!!
http://www.techpowerup.com/articles/other/22
Also, check all the places that your motherboard mounts to your computer case. Some times if one of the screws is a little off it can come into contact with traces on the motherboard and short it out causing it to not start up.
You can also do what I always do. Unplug all the components, ALL of them (even take out the ram, but leave the CPU in). Then start one by one plugging stuff back in trying to turn on the system after each component is installed. Start with nothing but the cpu, then plug in the RAM (some systems will not start without ram). Then video card, then hard drive and so on.
GOOD LUCK!!