Anna has an old Sony Vaio laptop that won't turn on anymore. Leo says that the battery may have finally died. Her laptop is pretty old and the battery may not be able to keep a charge. She should try taking the battery out and see if the laptop will turn on with the AC adapter. If it can't, she may need to get a new battery for it. They're about $90. That's a lot to spend on an old machine, though.
She should also try pressing and holding the on/off button for about 10 seconds. Then release and press again. This forces the computer to reset itself and turn it back on. if that doesn't work, then she should pull the hard drive out of it. She can then get the data off it that way.
Time to get a new computer. Leo recommends Dell or Asus, but she should also take a look at Chromebooks. They are less expensive, easier to use, and far more secure. Most people need only that.