my mac will not start

Contact Apple Service, iMac Service or Apple's Express Lane. Do note that if you have AppleCare's protection plan and you're within 50 miles (80 KM) of an Apple repair station, you might be eligible for onsite repair since yours is a desktop machine (depends on where you're located). BTW, the AppleCare Protection Plan's the best warranty policy available for desktop machines. Get it if you don't have it before contacting Apple.

There are a few of things you could try, but success is not guaranteed:

An SMC and PRAM reset:

https://discussions.apple.com/docs/DOC-3603

A Safe Boot:

http://support.apple.com/kb/ht1455

Booting into the Recovery HD to try to effect repairs to the HD with Disk Utility:

http://support.apple.com/kb/HT4718

IMO, it's tough to do those if the machine won't start up.

True, but an SMC reset has been known to kick-start an apparently dead Mac. And I did say it wasn't guaranteed 😉.