If I haven't used the computer in a while, and I hit the power button, I have a somewhat greater degree of confidence that the computer will start. However, I cannot truly say that the computer NEVER boots again quickly after it has booted once. But, as you said, I find it is less likely to boot again immediately if I have been on it for a LONG time after a previous successful boot. I have had no problems with the computer shutting off once it is on - aside for if the screen turned off for power saving reasons. I disabled the power saving features for now, and as long as the computer manages to boot, the experience is completely normal, everything seems to run fine.
Truth be told, though, I haven't really tried to use it for long spans of time since there are these problems. The longest I've used it since the not booting thing has become a real hassle is probably around three hours.
"if it is something you have done or feel you can do on this machine have you tried (don't need to remove it) disconnecting the cables to the CD drive and try booting it with them disconnected?"
No I haven't done this, I don't have a lot of confidence for messing around with hardware, although I tend to be a good learner when it comes to computer stuff. How can one do as you described? Or is there a webpage with good instructions for doing so? Even if it's something I feel I cannot do/should not attempt, I could at the very least enlist someone more hardware savvy than I to try it out.
Thanks for all your help!