I have no experience in laptops, and I have a couple of questions:

1) I left the system on standby for a couple of hours. When I returned, it wouldn't respond to anything I press. My guess is it went to hibernation mode.

2) On my desktop, I normally disable the hibernate option. From what I understand, when a system hibernates, it saves its current state and then shuts down. Turning the system back on should load the saved state. However, in my laptop, when I turned it back on, nothing happens.

3) Is there a way to get the system running again?

Even on standby, you usually have to press the power button, see if your computer supports acpi fully, maybe a bios update is needed, and see if you have the correct drivers for your chipset and processor