Hi,
From my experience with the no screen issue is that there is usually some piece of faulty hardware mainly the hard drive or motherboard.
I don't recommend swapping the CMOS Battery on the Toshiba as I do believe it is soldered on via two small cables.
Try plugging the laptop into an external monitor to see if the screen is dead.
Try removing the hard drive and boot it up.
Try removing one stick of ram if two are installed and boot it up.
Try swapping out which ram stick you remove and in which slot you install the ram into.
Hope this helps.
Waffles