How do I "zap the PRAM?"

Doing so is not likely to help, but see Resetting your Mac's PRAM and NVRAM.

Open Activity Monitor in the Utilities folder. Select All Processes from the Processes dropdown menu. Click twice on the CPU% column header to display in descending order. If you find a process using a large amount of CPU time, then select the process and click on the Quit icon in the toolbar. Click on the Force Quit button to kill the process. See if that helps. Be sure to note the name of the runaway process so you can track down the cause of the problem.

Then likely it means a problem with a third-party application you are using or an issue in your user account.

Create a new user in Users & Groups preferences with admin status. Log out of your account and log into the new account. Do you still have sleep problems in the new account? Be sure to disconnect all your peripherals except the keyboard and mouse.

I recently installed Mountain Lion and now our iMac works poorly. Most of the apps are really slow to open, if they open at all. I even have to wait several minutes for System Preferences to quiet down (spinner) enough to use it. All sound devices have disappeared, including the Internal Audio, even though the computer makes sound with no problem at bootup. Someone advises resetting PRAM, but that does not work either. The computer just keeps re-booting. If you have any solutions, or other ways to reset PRAM, please let me know, for my system has been dead in the water for three days now. Thanks.