There is a very good chance the Power Adaptor has died.
These usually go bad without a warning of any kind.
Does the Adaptor itself have an LED Light showing it's plugged in (some do, some don't)?
I know you said it's not warm any longer, if working it should be a bit warm to the touch (Not Hot)!

If the Battery depleted itself while you were on your vacation which it very well could have in
Hibernation Mode, your Battery will have no power or very little left (maybe not enough to Boot
the computer again, once it was run out).
If the Power Adaptor has Died, your Battery is now Unable to Receive a Charge from the Adaptor.
This doesn't necessarily mean the Battery is bad too, although they do die occasionally!

The advice above to Disconnect the Battery and try powering up with the Adaptor is good advice.
If it doesn't power up (which I imagine it won't) the Adaptor needs replaced.
You can pick one up on Ebay or Amazon much cheaper than you could in a Local Store or the Asus Website.