The laptop wouldn't shut down properly last night, so I closed it by the power button.... This morning I found that it was still TRYING to power off. The laptop was very hot, so I used ctrl-alt-del, and it booted to a black screen with a cursor flashing in the top left corner. I then hit the power off button to let it cool down completely. Upon trying to restart it again, it boots to the Toshiba logo, and then goes directly to the black screen. I've tried booting it with and without the battery, using AC only and it doesn't work. I've tried hitting F8 upon booting, and still nothing. I've examined the power cord, and it is ok. When it enters boot mode, the LED's come on including the HD. There is no beep sound coming from the computer.

If you have a desktop monitor, connect it to the laptop and boot it.

I tried that, and it still shows up with a black screen.

Chances are the video chip set is shot.

Wouldn't I not be seeing the Toshiba Logo come up in the beginning of the boot if the video chip was shot?

You might be right. I don't know if that's part of the POST or not.