Q: After restarting computer, in now comes to a grey screen and beeps 3 times without coming on.

Hi Jim...

"Beeps" means there's a problem with the RAM (memory). Three beeps means the RAM is bad and needs to be replaced.

Power On Self-Test Beep Definition - Part 2

You can purchase RAM online. Crucial comes highly recommended on these forums. You can use their scanner tool here >

SDRAM, DDR2 and DDR RAM memory upgrades from Crucial.com

And install yourself >  iMac: How to remove or install memory

Or take your IMac to an Apple store or Apple certified repair shop.

You can make an appointment at a Genius Bar in advance > Apple Retail Store - Genius Bar

edited by:  cs

Check your RAM, sounds like you have a bad or unseated module.

see > iMac: How to remove or install memory

Also please note that it is hard to give better instructions for troubleshooting or testing, because we do not know which model iMac you have or what OS X version you are running.