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 sure why.
If you are fortunate to have an access panel (I do not) on the bottom of the laptop, you can probably access the CMOS battery from one of the panels, likely the RAM panel. The battery is usually a coin cell, often CR2032, that is held in place by clips on the motherboard. Wearing an anti-static strip, simply pop out the cell and replace it with a new one.
If you are like me and don't have an access panel, you could try what I did and remove your bottom panel. Google removal bottom panel toshiba satellite for lots of advice. Basically just remove all the screws on the bottom of the plastic bezel and remove the battery if so configured and optical drive if one is present. I used a guitar pick to gently insert it between the plastic bezel and the motherboard layer and very slowly pry up the panel. Be careful here. It is easy to break the tabs that hold it all in place. Once the panel is off, look for the aforementioned coin cell on the motherboard. It is somewhat smaller than a quarter usually. If, like me, you don't have see one anywhere, then it is probably either hiding under some other component like the RAM, hard drive, or blower, or more likely it is on the *top* side of the motherboard. This is a real problem since I don't see an easy way to access this without either removing the keyboard assembly or completely removing the motherboard and disconnecting all the myriad connectors to gain access to the CMOS battery.
Now, at this point, we can wonder WTF, Toshiba?! This is the situation I find myself in. I have a L55D-B5364 Satellite, which has NO access panels. I removed the bottom panel to gain access to the RAM, which I was able to upgrade to 16GB, and to the HDD, which I replaced with an SSD, but no joy in finding the CMOS battery. I am not going to try to remove the motherboard just to get to the CMOS, so I still don't have a solution myself. If anyone has experience with this and has found the CMOS for this or a comparable model, please enlighten me as to how to access it. Toshiba Support refused to tell me any information regarding the CMOS battery, which seems in bad form to me...