Answer to: How to fix the screen?Before committing to the expense of a new screen, I would disassemble the stepped-upon part (presumably the screen) to inspect for damage. You might learn something useful. Maybe it is just the cable. Maybe some additional parts are also damaged and need to be replaced.
Answer to: No Power to ComputerYour battery is not the problem. I tested my Toshiba Tecra M3 laptop and with the power adapter plugged in it will boot up with a flat battery or even with no battery at all. Because your laptop showed signs of life only with the new power brick, the old one is probably bad. Rather than throwing out the old power brick, you should troubleshoot it and see if you can repair it. When you power on your laptop, listen closely. You should hear the hard drive spin up almost immediately. If your laptop has been without power for a long time, it will beep and prompt you to press F1 to reset the date and time. If your laptop is completely unresponsive, disassemble and check the power button. While it is disassembled, you can inspect for signs of the spill you suspect that your kids committed. You can find a link to the Tecra M3 manual here: https://support.toshiba.com/support/mode... On page 209 it says this: The computer will not start. Make sure you attached the AC adapter and power cord/cable properly or installed a...
Answer to: keyboard cursor moves jumps back while I am typingTroubleshoot this by typing with an external USB keyboard to see if the problem goes away. If it still happens, then try reloading Windows. If the problem goes away with an external keyboard, then consider operator error. Undesired cursor movement could be caused by inadvertently touching the trackpad while you are typing, with your fingers or the heels of your hands. If you are sure operator error isn't the problem, then a bad connection in the trackpad could be causing the problem. Troubleshoot this by opening the laptop and disconnecting the trackpad ribbon cable. Test to see if the problem goes away. If I recall correctly, the trackpad ribbon cable can be tricky to reattach if you go from the bottom (I had this problem with one of my Toshiba laptops). If this is the case, do some obvious disassembly and you will easily be able to reattach it by working from the top.