How do I turn on my iMac- it is acting as if it has no power even though it does.

Help! I have a two year old iMac. I turned it off before going out of town and it will not start again.

I push the power button and nothing,

It is plugged in with power.
All cables are correctly put in.
No lights go on.
There is power to the outlet it is plugged into.

Can anyone offer me advice? If I can just get it started once I swear I will never turn it off again!

PLEASE Do not tell me to get a PC or that my computer is junk. I need to use a Mac and I will not get the help I need if we end up having a pissing war on computer makers instead.

Thanks!