Let's start by looking at the mobo, is it installed in the case? If so make sure all mounting holes that can be used are used (normally six to nine) and have a standoff and screw used, no screwing directly to the case, need a standoff in each, otherwise mobo can short and cause problems (and when you reinstall, make sure the screws are good and snug, don't overly tighten, can crack the mobo.. Since a short is a possibility, lets pull the mobo and place it on a non-conductive surface, preferably on the cardboard, wood, newspaper, etc.
Check the CPU Cooler, in particular third party coolers and make sure no metal parts are touching metal mobo components like resistors, chipset covers etc. Remove the cooler and if you have the stock cooler get it handy. Then examine the mobo itself, looking particularly for scratches, scorches/burn marks, cut traces, swollen/leaking capacitors or loose components (chips, etc). Pull the CPU and make sure it’s aligned correctly and the notches lined up. Look for thermal compound that may have seeped to the bottom of the CPU. Check the socket and make sure there is no debris/thermal compound/dust or bent/broken pins and clean off the compound from the CPU and cooler, don't want to reuse old, (isopropyl (rubbing) alcohol works well).
Disconnect any cables for SATA, USB, etc. Just down to the bare mobo. If all looks good reinstall the CPU and attach the CPU cooler (carefully, don't want to overtighten the cooler, which can bend pins in the socket. Next, you should have two power cables going from PSU (Power Supply Unit) to the mobo, a large 20/24 (24 is more common on newer mobos) PIN connector and an 4 or 8 (8 is more common on newer mobos) PIN CPU power cable (and make sure this is the CPU Power connector cable and not a PCI-E connector for a video card - check the connector, I've seen where many have forced a PCI-E connector to the CPU power socket, and ensure it’s installed correctly in the proper orientation (each of these connectors generally always has a clip type protrusion on one side, when inserted it should lock down over the protruding lip that is only on one side or the female connection point on the mobo.
Add the GPU (graphics/video card) and if power cables are required from the PSU attach it/them (these generally are the same as the mobo power cables with a clip on the male cable from the PSU and a lip on the connections of the GPU card. . Cable it to a monitor and power on the monitor. Pull the CMOS battery (looks like a silver coin) out of the mobo, wait about 15 seconds and reinstall. Before installing any sticks, go ahead and try and power it up, fans should spin and if an on board speaker is there it should beep to let you know it’s trying to start but there is no RAM installed.
If that goes well, shut down and firmly install 1 stick of DRAM in slot 1, by that I mean by pressing it in the clip or clips on the side of the stick should lock in by themselves, you shouldn't have to click them closed by hand. Plug in PSU power cable and power up. If nothing at this point, may have a bad PSU, CPU or GPU. If another PSU is available or if you can borrow one, try that, no joy try same with GPU or try using on-board video if available. Still no joy, try a different stick of DRAM.
If all looks okay, shut down and plug in keyboard and mouse. If still OK, power down and add another stick of DRAM....Still okay add a single drive and try powering up. Continue with other devices. If there are any problems anywhere along the line that may well be the problem. When all installed and no problems, add another stick of DRAM, then the third, etc
Like to thank Essenbe for a couple add ons that I just entered.
and additional editorial thanks to Britton for additional suggestions just added
Additional suggestions welcome and can be added, it's sort of hard to think of that is done as it's more habit for me than thought, I throw (just kidding about throwing it, though at times I want to) it on a table and start running through actions, don't really even think about the steps any more..