My eMac's been having some boot-issues recently where it would sometimes just beep a couple of times and leave the screen black (the light on the front also blinking). Note that it does *not* put me into singe-user mode.
The behaviour matches exactly that of a RAM-problem described in
this Apple support article (though it's not the same generation), but wouldn't the issue then had shown from the start? I eventually got it to boot after having juggled the ram around for a bit. It shows the correct amount of RAM in the ASP, btw.
I had also placed a piece of foam behind the fan to reduce the noise from the it, could it be that it's gotten (temporarily or otherwise) overheated?