We've seen this in both Lenovos and Asuses, but sometimes if a laptop is very dead, it needs to be charged for a few minutes before it has enough juice to power on. Before chalking up a non-responsive computer to a physical issue, let it charge for 15 to 20 minutes and then press and hold the power button for a few seconds.
If after charging for 20 minutes the device doesn't turn on, it may need some TLC from the help desk.