jack, since the blue lights blinks 5 times then stops after the power button is pressed, it is an indication that the battery has drained out and unable to receive power from AC adapter, you may check by pluging the AC adapter to another working wall outlet. If the issue persist you need to replace the AC adapter. You may also perform the below mentioned power reset steps before replacing the AC adapter.
You may perform a power reset by unplugging the AC adapter from notebook, Turn the notebook over to remove the battery. Turn the notebook back over and open it, Hold down the power button for 30 seconds, then release the power button, Turn the notebook back over and slide the battery back into place, Slide the lock tab back into the lock position, Turn over the notebook one last time and plug in your AC adapter, Turn on your notebook. from [http://community.acer.com/t5/Discussion-Forums/ct-p/boards|here]