My computer will not boot, what is the problem

I have the EXACT same problem. I have a Gateway desktop, only a few years old. I don't have the model information right now. The problem started about 4 weeks ago and I was able to shut of the power on the power cord, wait a few minutes and try again and after about 5 tries, it would finally boot up. That bandaid stopped working about a week ago and no matter how many times I try, it will not boot up! The fan comes on as if it is working at full speed and the light comes on the computer. The monitor is working because the box with 3 colors pops up, (something about analog), and then goes in to what looks like sleep mode. I checked all cords, they are fine. Nothing looks too dusty. I don't think it overheated because I never left the computer on for more than a couple hours at a time. I didn't add any mods or make any changes at all to the computer before this started happening and have never had any problems with this computer since I bought it until now. What could it be and how can I fix it?