If you have a system that powers up, the next question is, do you hear any beeps coming from the motherboard speaker. If your motherboard doesn't have an integrated piezoelectric speaker but does have a speaker connection next to the power and reset connections (usually the front, left-hand corner of the motherboard) attach a case speaker. If you hear an unending string of beeps, it's often bad RAM, while a repeated sequence can be RAM or video. Other beep codes have been largely abandoned since they pertained to non-user replaceable surface mount components.
Beeps or no beeps, I always reseat the video adapter and the RAM, paying special attention to the locking levers on the memory sockets.
Are your motherboard settings on the defaults? Whether you just put in a new motherboard or have been fooling around with overclocking, restore the default settings. This is often accomplished with a single jumper or switch setting, but sometimes it involves moving several jumpers or switches. Get the default values from the motherboard documentation.
Unplug the power cable before each change in the case. Disconnect drives, one at a time, reconnecting power and trying power up after each. Next start removing adapters, saving the video adapter for last, reconnecting power and retrying after each change to ensure you discover which component is causing the failure.
Running the motherboard without a case is a common technique used by technicians to eliminate any weird grounding and shorting issues or mechanical stresses. It also makes it much easier to swap the CPU if that's required. I normally do my bench testing on top of a cardboard box, with a static free bag or foam between the bottom of the motherboard and the cardboard. You don't walk away from a test like this or you might come back to find the box on fire! If your motherboard powers up on the bench with the same power supply that you used in the case, you have a geometry problem. Ideally, you should have a spare power supply for bench testing if you're going to do regular repair and testing work.