Wow. Thanks for all the information. I'm sure we can determine exactly what your problem is based on "blue light on but no display". Maybe a little more information, might be helpful.
Like, how old is the machine?
What is the model number?
What is the model number of the power supply, which should be printed on the power supply itself?
Did this happen suddenly, or were there some warning signs that something wasn't right?
Did you make any changes to any hardware before this happened?
My first guess would be that the power supply has died, and having an LED on is no indicator that it's working. Fans don't necessarily mean anything either. Has the CPU fan heatsink ever been cleaned out or is it packed with dust and junk? Take the...