I'm having the same issue. Not sure when it started, exactly (I'd say several months ago), but it seems that *most* of the time I power down my PS3 now, it shuts completely down and doesn't go into standby mode. In order to turn back on, I have to flip the rocker switch off and on on the back of the machine.
Sometimes, when I flip the rocker switch off and back on, the red light will come on, but won't allow me to turn the machine back on. As soon as I try to power up (either with the soft button on the front of the PS3 or with the remote), it goes immediately back into the powered off mode. In these instances, I find that I just have to wait in order to be able to restore power to my console.
**I have the same original 80gb model that you mentioned.**
My speculation is that it might be overheating, but I have it in a well-ventilated area. I use my PS3 primarily for watching movies.
Anybody else having these issues? Any other suggestions for fixes?