I have a Toshiba Satellite laptop which was bought in 2003. The laptop
is experiencing some problems and is not able to power on. I am
looking for a service plan which is less than 100 dollars which will
cover this particular problem.

I am not aware of any insurance you can buy after-the-fact.  The cause
of your problem is most likely going to be a bad powersupply or
motherboard but to know I would need to have a better understnding of
what the laptop does when you try to turn it on (does it spin up? do
lights come on? fans?).  The prices of laptops have dropped drasticly
so if the cost to repair is pricey you may want to just look into
getting a new laptop and pull ther HD out of the old one and
recovering any important information from it onto your new one or onto
a desktop.  An option you may want to try exploring is contacting
Toshiba and seeing if they will offer you an exended warrenty on the
laptop.