Try each one in this general order until problem is fixed:
1) check all your connections including your memory, power connectors, cards, fans and ensure the 4-pin connector for your CPU is installed if your system requires it. If you have removed your memory, make sure it is the correct slot(s). Not all slots work. I don't know if this will prevent the computer from trying to boot. At any rate, every motherboard manual details exactly how RAM should be installed for that particular board. If problem persists:
2) test the power connection with a lamp
3) make sure your on/off switch (if you have one) on your power supply is ON
4) remove the cables from ALL drives and restart
5) also remove unnecessary cards and non-cpu fans
6) Borrow a power supply (sufficient power and appropriate 20 or 24-pin connection)
I've seen this happen when a connector is improperly placed. The motherboard and/or power supply can detect an inappropriate power surge and not even start.
Some people have accidentally joined power connectors to each other, usually when hooking up system fans.
Your system can turn on and start booting to the BIOS with only the motherboard, a power supply and I assume some RAM (though I'm not positive the RAM is requied). It does not even need the monitor, although you obviously won't see what is happening but you will hear the power supply start. In general, with such a fault if the problem is not immediately obvious you should start with only the absolute bare essentials and, if your system starts add your components a few at a time.
Also, it is best to clean the exposed computer parts with compressed air.