If you have two RAM sticks, try booting with just one at a time. Try booting without any RAM and also with the hard disk (and any other drives) disconnected. Take the front cover off your PC - this should expose the power button, make sure it is clicking correctly when you switch the PC on. If you have a spare PC, try using your RAM in that to test it. Also try connecting your hard disk as a slave.
You have already ruled out a faulty PSU, if you can also rule out faulty RAM and HDD, it will be either the CPU or motherboard that is at fault.