Remove all of the memory sticks and power the system up. If you have a speaker attached to the motherboard, you should hear 3 beeps. If you do not hear any beeps, check your motherboard manual to find out where the speaker attaches,and attach one. If your motherboard did not come with one, amazon has them for as little as $4.49 and some of those have a bunch of them in the package.
Most systens will use a speaker that looks like this
If there are no beeps with the memory removed, and speaker attached, it could be the motherboard, the CPU or even possibly the power supply (or the power supply connectors improperly seated).
Before you start doing the items below, remove everything from the system except the CPU, power supply and that speaker that I talked about above. Disconnect all drives, video cards, USB devices, everything that draws power. We are trying to remove all other devices that might possibly be stopping the system from booting up. And we want to see if you can get the beeps of any kind.
Cheapest first thing to do if there are no beeps it to remove and reseat the two motherboard power supply connectors. Those are the 24 pin and 8 pin connectors. Both of those cables are thick, stiff cables and need to snap into their sockets. These cables are tough to work with at times, but this is really the only free fix among the choices you have.
Next cheapest step is most likely to be replacing the power supply itself item.
Following that,will probably be the motherboard itself. While you have the CPU off of the motherboard, check the pins on the CPU to make sure none are bent or missing. If there are bent pins, you may be able to bend them back straight, but watch some YouTube videos on how to successfully do that.
And finally the last thing I see as likely possible, is the CPU itself.
At some point, you should begin to hear the beeps. When you do, add the video card back in, and make sure the system still beeps with that installed. And repeat the attach a single item, reboot and listen for beeps after each and every item. Eventually either something you attach will cause the system to stop beeping and you will found the problem device, or you will eventually add the memory back into the system, and the system will magically fixed itself and boots up for you.