I have had this iMac for about 3 1/2 years now and it started acting really slow the other day. I was not home when it started on Friday evening but it looked like it restarted and I had an blue screen for at least 20 minutes. I shut it off and rebooted the next morning and it took about 45 minutes to get from the load screen to the desktop. It feels extremely hot on the back so my thought was that the fan had stopped working. I tried to run some software and nothing works. . . . What should I do?

Have you repaired Permissions lately? That's where I would start. Open Applications/Utilities/Disk Utility and select Repair Permissions. If you haven't done this in a while, or never, it might take some time. This will put lots of bits and pieces back where they belong.
Also, the number of things you have on your desktop can make you computer slow in booting up.
If you find that you still have problems, get the original install disk, boot from that ( hold down the "c" key while booting, and run Repair Permissions from that. You might want to run Check disk or Repair Disk, depending on what happens when running the others. Be sure and back up anything that you can afford to lose, just in case!

I think you helped me out with a dozen or so math problems.

Its a common problem, dont worry.

go to system preferences- startup disk and reselect and restart with the OS X volume.

I have had this iMac for about 3 1/2 years now and it started acting really slow the other day. I was not home when it started on Friday evening but it looked like it restarted and I had an blue screen for at least 20 minutes. I shut it off and rebooted the next morning and it took about 45 minutes to get from the load screen to the desktop. It feels extremely hot on the back so my thought was that the fan had stopped working. I tried to run some software and nothing works. . . . What should I do?