This model of Toshiba Satellite lacks an access panel on the bottom of the laptop, so I removed the bottom panel of the...

This is what my motherboard looks like after removal of the bottom panel. I don't see a coin cell on here. Perhaps it is hiding under the cooler or it's on the top side just under the keyboard. What do you think?

I think that it is likely the CMOS battery has become charged down. I had a similar problem where I didn't use the laptop for several months. When I tried to turn it on, I would get the same results. Try this. Remove your main battery from the computer, hold down the power button as Jeff suggested for about 30 seconds, then plug in your AC adaptor without the battery and charge for 12-24 hrs. Hopefully, your CMOS battery will be charged. Are you able to access your BIOS? Try F2 or F12 repeatedly before the Toshiba logo appears. I was getting messages about the RTC clock battery having a low charge. Try connecting an external USB keyboard if you are unable to get into the BIOS by hitting the appropriate F keys. This is what I had to do to get it to connect to BIOS and reset my date/time. Then it would boot. Also, check whether or not you are using sleep. Sleep doesn't play well with laptop when turning them back on in my experience, and I disable it altogether. Generally, hibernate works ok, though. Not...