I have the same issue with an old Satallite at home, where the power button stuck and eventually broke. I have popped the case open to take a look at the actual button, which is small and has a rubber cap on it. I used a pen for a few months to turn it on, which eventually ripped the rubber bit off. Now I leave the laptop on, as it will take me about 10-15 minutes to turn it on otherwise.
You will not be replacing the motherboard just for this tyny switch. Unlike the small card that was $50 in wahnula's camera, this switch is on the motherboard, and the cost of replacing it will run you about the same as picking up a cheap new laptop at Circuit City (figure $700 if you sent the laptop out and had the motherboard replaced).
What you may want to do (as I should do, since I'm in the same boat but too lasy to do it), is look on ebay, used stores, etc., for another Toshiba laptop that is the same model as yours. If it's cheap enough, buy it and use your old one as parts. If it doesn't work and real cheap, buy it for parts to fix your laptop. I recommend you do this soon though, as once that little rubber bit pops off, a new button probably won't help, and resoldering a new switch on a motherboard will not be fun.
Jarrett