The trick you used in the beginning was a bios HARD reset and is used when your BIOS is in an unfix-able and unchangeable state. This works find but if your BIOS was having issues before you may have only treated the symptoms. I have worked with the BIOS on a few of these Toshiba's and i found that the BIOS is often in need of an update. First you want to make sure you can even get to the BIOS at this point, or at least get some screen activity.
I have a few things you might check to make sure there are not any other issues.
Press and HOLD ESC and press the power button, assuming that the screen is not damaged or the back-light has failed. Hopefully you will see something on the screen, this is a diagnostic and you should see some info on your memory, HD, and CMOS checksum errors if you have any.
If this does not work get a very bright flashlight, something in the range of 120 Lumens if you can. Boot your computer while holding down F2 for a short while. Shine the flashlight into the screen at a very close distance and move it around. You should either see your BIOS screen, a very black surface with no traces of light, or a much lighter area that looks light brownish. If you can see your BIOS screen GREAT, you most likely have an issue with your screens inverter board which you want to address first. (However given that you have attempted a external monitor i feel like the changes of this might be slim)
If you have a very black screen move the flashlight to the very top left and see if you can see any text. Since your view is limited to about a half inch area around your flashlight you may want to redo the ESC / F2 boot method while searching for text this way.
When you first boot your computer the LCD panel should be transparent to a degree and most of the light will be able to pass through onto the very back of the panel (which looks light brown) now when your computer starts up the VIDEO CHIP signals the LCD to blank or turn black (opaque) or not transparent and your light will fail to pass through to a degree. Now this is important to note because if your VIDEO CHIP is damaged then the screen will fail to switch from the transparent to opaque. (Please keep in mind that some LCD panels don't behave like this so they may appear opaque the entire time. Which can make the diagnosis a little difficult.)
Let me know what happens if you can, you may have issue with your BIOS but if you cant see your screen then its going to be difficult to figure out what it is.