Q: Major Boot problem!

See:

Mac Maintenance Quick Assist,
Mac OS X speed FAQ,
Speeding up Macs,
How to Speed up Macs,
Macintosh OS X Routine Maintenance,
Mac troubleshooting: What to do when your computer is too slow,
Essential Mac Maintenance: Get set up,
Essential Mac Maintenance: Rev up your routines,
Maintaining OS X, 
Five Mac maintenance myths and
Myths of required versus not required maintenance for Mac OS X for information.

Then,

Have you tried running Apple Hardware Test to see if there are any detectable physical problems with your iMac?

Best of luck.

Back up all data immediately, as your boot drive may be failing.

If you have more than one user account, these instructions must be carried out as an administrator.

Launch the Console application in any of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad. Click Utilities, then Console in the icon grid.

Step 1

Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left. If you don't see that menu, select

View ▹ Show Log List

from the menu bar.

Enter "BOOT_TIME" (without the quotes) in the search box. Note the timestamps of those log messages, which refer to the times when the system was booted. Now clear the search box and scroll back in the log to the last boot time when you had the problem. Select the messages logged after the boot, during the time something abnormal was happening. Copy them to the Clipboard (command-C). Paste into a reply to this message (command-V).

For example, if the problem is a slow startup taking three minutes, post the messages timestamped within three minutes after the boot time, not before. Please include the BOOT_TIME message at the beginning of the log extract.

If there are runs of repeated messages, post only one example of each. Don’t post many repetitions of the same message.

When posting a log extract, be selective. In most cases, a few dozen lines are more than enough.

Please do not indiscriminately dump thousands of lines from the log into this discussion.

Important: Some private information, such as your name, may appear in the log. Anonymize before posting.

Step 2

Still in Console, look under System Diagnostic Reports for crash or panic logs, and post the entire contents of the most recent one, if any. In the interest of privacy, I suggest you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if present (it may not be.) Please don’t post shutdownStall, spin, or hang logs — they're very long and not helpful.