No startup - two E8400 CPU boards

I know there are a lot of "my computer won't start" threads on here, but I'm at my wits end on two separate boards both running Intel socket 775 E8400 CPUs.

One will start up intermittently (Gigabyte EP43UDL); the other will not turn on at all (Intel legacy board).

I've already done the following:

* Changing out DDR2 to tested working sticks.
* Using an alternate tested power supply.
* Disconnecting the HDD.
* Checking the CPU fan and case fans.

My questions are:

* Would a CPU failure cause these issues?
* Are there any known issues with the E8400 CPU failing and causing problems like these or is it just coincidence?

I'm thinking about ordering a used E6400 to run tests with; however I don't want to waste the money if it is unlikely to solve the issue.

Thanks in advance for your help.