warbladex, welcome to the forums.  What you are seeing could be as a result of a bad motherboard, power supply or another peripheral and it's going to take some process of elimination to see which it is.
 
Easiest step is to disconnect your non-essential components.  If you get the system to stay on at this point, add them back in one at a time and test between each.
 
Should there still be problem, try reseating the components that are still installed, power connections included.  If needed, take the system down to a single stick of memory and swap it out as needed.  If removing memory helps, test the ram slots individually.  This is almost as far as we can get while still allowing for an image to come up, any time past this we'll be looking for a change of behavior or a POST code on the LED readout.
 
Remove the GPU.  Sometimes this will allow the system to stay on and if it does you'll want to try it out on another machine or try out a spare GPU.  Any other behavior you see, let us know.