The other day I shut down my computer. (Intel iMac matte screen, 10.4.11) Later, when I pushed the restart button, I failed to get a bong & the sleep light started blinking rapidly & bright. For a number of times I held down the restart button to get it to shut down, & then pressed it again to restart...same blinking light. (I've never seen this behavior before) I managed to finally get it to restart by double clicking on the restart button, but I don't even know why I tried that.
If and when it happens again, note if the LED is flashing once per second or three flashes with a pause. See the [Intel iMac Startup sequence|http://docs.info.apple.com/article.html?artnum=303363] article.
The hardware tests from your [Install Disk 1|http://docs.info.apple.com/article.html?artnum=303081-en] or [TechTool Deluxe|http://www.micromat.com/index.php?option=com_content&task=view&id=199&It emid=104] can be used to test the ram.