Q: Continous spinning pinwheel?

Likely one of two things. Failed hard drive or bad directories. Do you feel comfortable with disk repair? If not, I might recommend taking it to an authorized service provider or to an Apple Store.

And to verify the issue, does this happen when you turn the computer on?

I apologize and redact that previous statement although it might have some merit in the end.  I would recommend forcing the computer off by pressing on the power button for a couple of seconds (about 10).  When it is off, turn it back on, but this time as it is turning on reset PRAM (resets the disk to which it is supposed to boot up to).

To do it, check out this article: http://support.apple.com/kb/ht1379

Link provided by bleezy1991 sloved my pinwheel problem!  You saved my weekend!!  Thank you, thank you!!

Thanks bleezy1991, this worked for me as well.

I would have had user use Recovery Mode, repair the system volume and also by clicking on top level of the hard drive to check partitions; then use Safe Mode on first boot.

After clearing nvram, you will need to reset the startup disk control panel.

Recovery Mode

Startup Manager: How to select a startup volume

http://support.apple.com/kb/HT131

Troubleshooting: My computer won't turn on

https://support.apple.com/kb/TS1367

Symptoms

If your Macintosh computer won't turn on, here's how to troubleshoot it. Please keep in mind that although your computer may display similar symptoms that prevent it from showing video, this article discusses what to do if the computer won't turn on, meaning that when you press the power button:

General purpose Mac troubleshooting guide:

Isolating issues in Mac OS X

Starting the computer in "safe mode":

Mac OS X: What is Safe Boot, Safe Mode?

To identify potential hardware problems:

Apple Hardware Test

General Mac maintenance: