iMac running Yosemite produces spinning pinwheel of death & freezing after two minutes

Greetings wise wizards of EE:

A friend of mine has asked me to help with her 27", Intel Core Duo, 4 GB iMac, which is running Yosemite. Approximately two minutes after start up it produces the dreaded spinning pinwheel of death animated cursor, and at that point it freezes, with no keyboard commands or mouse activity at all. At that point, all that can be done is to perform a forced shut down with the power button. Here's what I've tried thus far:

1. I booted to safe mode, but the issue persists, and after the same amount of time
2. I removed all Login programs, so nothing is set to auto-load (that I am aware of), but the issue persists
3. I took a look at the Applications folder, and there are no obvious forms of junkware that I am aware of
4. I used the Command + R keyboard command to boot to what I assume is a diagnostics partition, to run the Disk Utility; under the First Aid tab, I ran verify permissions, repair permissions, verify hard drive, repair hard drive; the latter two stated that the drive appeared to be okay.

That's what I've done so far, and the issue still persists. Please sing out with any suggestions on how to solve this highly annoying issue.

Many thanks in advance,

Zovoth
zovothAsked:
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David AndersTechnician Commented:
Examine the system Logs with Console (Applications > Utilities)
http://pondini.org/OSX/Logs.html
Test the Ram
http://www.cnet.com/how-to/how-to-test-the-ram-on-your-mac/
Make a Genius appointment and take it into Apple Store
https://www.apple.com/retail/geniusbar/
Do a clean yosemite install on a partition or external drive and test

Revert to Mavericks - assuming a Time Machine backup
http://osxdaily.com/2014/10/22/downgrade-os-x-yosemite-to-mavericks/

What should have been done to prepare for Yosemite
http://www.macissues.com/2014/09/08/how-to-prepare-for-and-upgrade-your-mac-to-os-x-yosemite/#more-1939
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strungCommented:
You could also create a new admin user and boot using the user to see if that makes a difference.

However, I agree with davidanders that the first step is to check the system logs to see what is happening immediately before the freeze. You could also try opening Activity Monitor, sorting the processes by CPU usage and see if something spikes just before the freeze.
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zovothAuthor Commented:
Greetings davidanders and strung:

My many thanks for your rapid response to my inquiry, both of which are helpful. I'm going to suggest to my friend with the clean Yosemite install... if the issue persists, at least it should isolate the issue to the hardware.

May the wind be at your back,

Zovoth
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