|"Did everything correctly in assembling the system"|
That would mean you benchtested your hardware 1st, right? Because if you didn't, everything else you're doing is just a waste of time.
"What is the probability of getting a bad CPU right outta the crate"
What is the probability of getting two bad boards "right out of the crate"? Going back to my other comment...if you're not benchtesting BEFORE installing the components in the case, you're wasting your time.
Maybe you don't know how?
1. lay the board on a non conductive surface on a table or work bench.
2. install the CPU w/HSF & ONE stick of RAM.
3. connect monitor to the onboard video.
4. plug in a keyboard...preferrably PS/2.
5. connect the PSU.
6. switch on the power to the PSU & monitor, then jump start the board with a flat screwdriver by momentarily touching the blade to the two pins the power switch would normally connect to. The PSU should instantly fire up & the POST screen should display. You can then use the keyboard to configure the BIOS settings & monitor the CPU temp.
Once you've confirmed it works to that point, shut it down. Then install the PCIe video card & the rest of the RAM. Power up again & make sure you're getting a display. At this point, most people would shutdown & put the hardware in the case. Personally, I would connect a floppy drive (you do plan on installing a floppy, right?) & run memtest86 to confirm the RAM is good. Yes, you can do it from a CD, but you're gonna need the floppy to install the SATA drivers during the Windows installation. It will also come in handy for updating the BIOS or running diagnostics.
Anyhow, if the system doesn't fire up outside the case, it's obviously pointless to install the hardware in the case, so you just saved yourself a lot of work & aggravation. And since you're basically testing just a few of the main components, it *should* be easier to narrow down which one is bad.
"Aptivia 680 Watt PSU"
Do you mean APEVIA? They used to be know as ASPIRE but they got caught misrepresenting their 500W units & there were numerous failures & consumer complaints. They changed their name to APEVIA stating that the reason was to prevent confusion with the Acer Aspire. If you can't get the board to post outside of the case, the 1st thing I would suspect would be the PSU.