Beachball keeps coming up

Help us help you. Which iMac? What Mac OSX version? iMacs have been in continuous production since 1998 in four broad families, each with different troubleshooting methods.

Doing "About this Mac" will show your processor type and the installed OS version. If the computer will not start, you can enter the serial number into this Apple supoprt page:

https://selfsolve.apple.com/agreementWarrantyDynamic.do

and it will return the model details. Post them here but do NOT post your serial number in open forums like these.

Some Macs are too old for Apple's lookup function. If the Apple page comes up with nothing found, you can use this third-party site instead--it works for older models as well as recent ones:

http://www.everymac.com/ultimate-mac-lookup/

For what it's worth, this forum areas only covers iMacs made from 1998 to 2005. If yours is newer, we can ask the Hosts to move you to the other forum which is much more active.