Laptop won't respond

Hello,
I have a toshiba satellite a105-s2081 laptop. It will not start up. When battery is in, the yellow battery indicator light flashes on and off but laptop won't come on. When a/c is plugged in (with or without battery), absolutely nothing happens. I bought a new battery, that didn't solve it. Tried the 30 second hold down the power button trick, that didn't work either. I'm assuming the old battery is toast, but don't know why it won't work with the a/c cable plugged in or the new battery is inserted. Any help would be much appreciated. Thanks in advance.