I don't like repeating steps that I've already put so much time into putting in the checklist, but here it goes:
#2 on the checklist is by far the most common mistake. Are you sure the 4/8-pin CPU power connector located on the upper edge of the motherboard near the CPU socket is fully plugged in?
Did you carefully follow the instructions on how to install the HSF? Is the HSF tight with little to no wiggle room? It doesn't take long for the CPU to overheat and shut down the system if the HSF isn't installed correctly.
Are you sure the CPU is installed fully in the socket and in the right direction? Were there any bent pins in the CPU socket on the motherboard?
Did you try each stick of RAM by itself and are you absolutely sure you're using the correct RAM slots?
Like jsc said, there's really no way of telling what the problem is without a $2 system speaker. They're worth their weight in gold in a situation like yours. I HIGHLY recommend getting a system speaker unless you want to randomly start replacing perfectly fine components like a lot of other people.
Do you happen to have a PSU from another computer that you can try? You can't put much weight behind Newegg reviews, but one reviewer of your PSU on Newegg said they solved a similar problem by using a different PSU.