Sounds to me like you have incorrect or faulty RAM DIMMs installed in your PC. Try removing or reseating one or more of them and let us know what happens.
You can do the below too
Firstly check to see the motherboard if power by looking for LEDs on the board, they should be on if the PC is plugged into power, even if the PC is not actually running. If no LEDs show when the PC is plugged into power and turned on at the wall on PSU, chances are the motherboard is dead.
1 - Check to see if the switch on the back of the power supply is switched OFF. If it is, turn it ON, hey presto, PC works! (this nearly ALWAYS gets me!!)
2 - Check to see if you have accidentally dislodged or forgotten to plug in your power switch wires into the motherboard! It's the simple things to look for first!
3 - Failing that, check to make sure everything is plugged in. Check 24-pin motherboard power and 4-pin/8-pin (depending on PSU and motherboard) CPU power connector especially. Also check 6-pin PCI express on graphics card if there is one
4 - If there is a floppy drive, remove it or unplug it.
5 - Start removing or reseating any extra PCI expansion cards such as modems, additional USB card, sound cards etc etc. Remove one by one and test to see if the PC will boot after you have removed. Eg - remove sound card, see if the PC boots, if it doesn't, remove modem, see if the PC boot etc etc.
6 - Start reseating or removing RAM sticks or try RAM in different combinations/bays. I recommend doing this first for your machine.
7 - Remove or reseat any dedicated graphics cards and see if the PC will boot using the onboard video if the motherboard and CPU support it. If not, remove the graphics card, install it temporarily in a known working PC, and see if the PC boots with it installed. If it doesn't boot with the card installed, there's your problem.
8 - Remove the CMOS battery and reinstall it a minute or two after you have removed it
9 - Try another known working power supply or remove the power supply installed in your system and try it in another known working system and see if you get the same problem.
You must make sure you ground yourself before doing any of this stuff. Plug the PC into power, make sure the power is turned on at the wall, touch a part of the case that is bare metal (a screw usually works) and then you are done. Try not to move around too much as you will build up charge again. To ground yourself again, just touch the same screw or bare metal part of the chassis you touched before.