Startup problem mid 2007 iMac
Can't get past login screen I just get the Beachball, I can access guest login
iMac (20-inch Mid 2007), OS X Yosemite (10.10.3)
If you still have them use disc 2 from the original install discs that were delivered with the Mac and Using Apple Hardware Test - Apple Support, run AHT in extended mode 2-3 times back to back. If it finds errors (as I believe it will) that means the machine has suffered a hardware failure. The reason to run AHT multiple times is it does not always find errors after the first or second pass, however when it does they are correct.
Due to the computer being 8 years old, you may want to consider replacing it. However if it's only a hard disc that has crashed then you can take that to an Apple Authorized Service Provider and have it replaced if you want.