Agree that CPU is not very likely your problem. But be advised that the power supply is quite often the culprit in these cases. The fact that some things turn on is by no means a guarantee that the PSU is supplying sufficient juice to your system! Test that PSU before you get another MOBO! I'd test the video card too before I tear it apart and order a MOBO. http://www.tomshardware.com/forum/245263-31-build-failure#t1745585
Testing the CPU and video you'll need to put them in a known working system, same thing with MOBO, known working PSU, RAM, CPU and video.
Easiest thing to test if you do not have replacement parts to switch in is the PSU. Buy one at a big box store, test the system with it, and then return the PSU if that wasn't the problem
You can also take your parts to a friend or else a local shop and have them test them one by one.
Please note that as sytemlord pointed out above there may be something else stopping you. Be sure to reset cmos and also unplug the system for a while, press the power button while the system is unplugged, plug it back in and try again.
I take it you get no error beeps or lights? If not I'd suspect either mobo or psu are stopping you very early on.