Other stuff is covered above.
An incompatible CPU is capable of causing a complete failure to boot. I have had it happen several times, and most recently with a system I built last week (the 68 chipset motherboard wasn't Ivybridge compatible without a BIOS update).
Incompatible memory (without the voltage being set to suit in the BIOS) can also cause a complete failure to boot. Only having 1 stick of memory when a pair is needed, can cause a system to fail to boot.
What device do you think the POST starts with? The GRAPHICS. If the card is not slotted right (over tight, angled in the slot wrong, seated in the slot wrong), or the card is dead, or the card has insufficient amps from the PSU to fire up, the system will fail to boot (in this case you may get a bit of a giveaway with a slight 'twitch' of movement with the CPU cooling fan - but with automated fan control where fans won't start up until what they need to cool has warmed up, that useful hint is often denied us now). So unscrew the card, take it out of the slot, wipe the contacts carefully, CHECK THE SLOT is clear and clean (no trimmed bits of production plastic insulating contacts), reslot it securely, but do not fix it firmly, so there's a little leeway to flex it side to side with the power on, and you hold the power button in. Sometimes people just fail to seat the graphics card at all, because the contacts in the slot are stiff, and the card is just sitting on top of them doing nothing. Is the monitor actually compatible with the graphics card? Not happened to me (I live and breathe system compatibility), but I have heard of grief caused by a monitor that was deeply disturbed at what it was being fed as signal. So never rule anything out. It's handy to have a known good basic graphics card around that doesn't need extra power from the PSU too.
Don't forget to check the fuse in the main power lead, or that it is seated fully into the socket in the PSU. If using an extension block of sockets (surge protector, etc), make sure it is actually switched on.
Only plug in the absolute minimum to get the system to post. Don't plug in DVD drives, hard drives, or anything else unnecessary to getting a successful POST. If it posts without the clutter, switch off, and then go through the process of adding one item at a time. The most surprising things can turn out to cause a boot failure.
Sometimes, a system just gets 'claustrophobic' after being in little cardboard boxes for sometimes months, or gets deeply unhappy with the inability of the delivery driver to traverse highways and road obstacles safely, and without screaming. When this 'system panic attack' happens to me, I call my fellow computer building buddy in the local town, and tell him to put the kettle on, as I have a system that wants a day out to see the scenic route. More often than not, I put the system on his bench, and it fires up immediately (you will not believe how often this has happened over the last 20 years or so), and never gives a problem after. Yes I get the 'put the kettle on' call from him now and again too.
Good luck with it, don't end up like me, with all my hair ripped out years ago.