IMac beachballs on startup for upwards of an hour

Question

My iMac takes ages to become operational, and for sometimes over an hour, it beachballs or simply freezes. However, if I leave it on, the problem seems to go away. it's been doing it for for a while on and off. I thought it might be an OSX issue, so upgraded to Yosemite from Mavericks but it's still happening.
I've verified the disk- no problems. I've verified and repaired a few permissions- still doing it. I've checked the RAM using Rember which came up with nothing either. PRAM/SMC reset too.  I'm a bit stumped.
To quote Penelope Pitstop- HAYELP!!
iMac 4GB 667 MHz DDR2 SDRAM
2.4 GHz Intel Core 2 Duo
Yosemite
Cheers for reading

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the 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
For this step, the title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
In the top right corner of the Console window, there's a search box labeled Filter. Initially the words "String Matching" are shown in that box. Enter "BOOT_TIME" (without the quotes.)
Each message in the log begins with the date and time when it was entered. Select the BOOT_TIME log message that corresponds to the last boot time when you had the problem. Now clear the search box to reveal all messages. Select the ones logged after the boot, during the time something abnormal was happening. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing 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—not at the end.
If there are long runs of repeated messages, please 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 don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.
Step 2
In the Console window, select
          DIAGNOSTIC AND USAGE INFORMATION ▹ System Diagnostic Reports
(not Diagnostic and Usage Messages) from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar.
There is a disclosure triangle to the left of the list item. If the triangle is pointing to the right, click it so that it points down. You'll see a list of reports. A crash report has a name that begins with the name of the crashed process and ends in ".crash". A panic report has a name that begins with "Kernel" and ends in ".panic". Select the most recent of each. The contents of the report will appear on the right. Use copy and paste to post the entirecontents—the text, not a screenshot.
I know the report is long, maybe several hundred lines. Please post all of it anyway.
If you don't see any reports listed, but you know there was a crash or panic, you may have chosen Diagnostic and Usage Messages from the log list. Choose DIAGNOSTIC AND USAGE INFORMATION instead.
In the interest of privacy, I suggest that, before posting, you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if it’s present (it may not be.)
Please don’t post other kinds of diagnostic report—they're very long and rarely helpful.