Q: My iMac won't turn on properly.

Beeps can mean the RAM (memory) is failing or has failed and needs replacing.

Power On Self-Test Beep Definition - Part 2

Welcome to Apple Support Communities

It looks like RAM is defective > http://support.apple.com/kb/HT2538?viewlocale=en_US&locale=en_US

If your iMac is in warranty, take it to an Apple Store or reseller and it will be repaired free of charge.

If it's not in warranty, you have to buy RAM. You can find RAM at OWC or Crucial > http://eshop.macsales.com/shop/apple/memory/iMac To install RAM > http://support.apple.com/kb/HT1423?viewlocale=en_US

If after installing RAM your iMac doesn't start up, take it to an Apple Store or reseller. Probably RAM slots are defective