It sounds like one or more of your parts may be broken or incompatible with your system. It could be anything, but I'll try to help narrow it down.
I don't believe the problem lies with your case. However, if you can't turn the system on at all, you may want to try shorting the power pins on the motherboard. If this works, then that means that the power switch is dead.
However, more than likely, the issue may lie in your PSU, RAM, or CPU. Double and triple check that they are working correctly (I once had a broken PSU that tested fine) and that all of your parts are confirmed to be compatible with your motherboard. It is likely you can google your motherboard and get a list of compatible hardware for it.