Suuuuuper slow iMac! Ran etrecheck... now what?

Question

I have an early 2009 Mac that has always been really reliable, until it was turned over to a certain family member for their main use.  I needed to use it today, and discovered it was running really really slow - even just minimizing a window takes a full minute to accomplish.  Even to get "about this mac" window to open takes several minutes.  I asked this person what they had been doing with it - apparently they have downloaded all sorts of pirated movies, audio and goodness knows what else onto it.  I'm furious, and trying to find whatever is causing the problem(s) and get it(them) cleaned off.
I found some other threads here where people complained of similar issues, so I followed the steps that were advised to them.  There is plenty of memory free, and I ran both verify permissions and verify disk and both of those came up with no errors.  I saw another thread that advised running etrecheck to get a list of whatever is on this Mac for diagnostic purposes.  It has been about thirty minutes, and etrecheck is still stuck at "checking kernel extensions".  The little wheel at the bottom of the window is spinning, indicating that it's still processing, but I don't know if the computer is just too infected to continue or what. 
Any suggestions?  I appreciate any help I can get.  

Answer 1

Back up all data to at least two different storage devices, if you haven't already done so. One backup is not enough to be safe. The backups can be made with Time Machine or with Disk Utility. Preferably both.
Erase and install OS X. This operation will destroy all data on the startup volume, so you had be better be sure of the backups. If you upgraded from an older version of OS X, you'll need the Apple ID and password that you used, so make a note of those before you begin.
When you restart, you'll be prompted to go through the initial setup process in Setup Assistant. That’s when you transfer the data from a backup.
Select only users and Computer & Network Settings in the Setup Assistant dialog—not Applications or Other files and folders. Don't transfer the Guest account, if it was enabled.
After that, run Software Update.
If the problem is resolved after the clean installation, reinstall third-party software selectively. I can only suggest general guidelines. Self-contained applications that install into the Applications folder by drag-and-drop or download from the App Store are usually safe. Anything that comes packaged as an installer or that prompts for an administrator password is suspect, and you must test thoroughly after reinstalling each such item to make sure you haven't restored the problem.
I strongly recommend that you never reinstall commercial "security" products or "utilities," nor any software that changes the user interface or the behavior of built-in applications such as Safari. If you do that, the problem is likely to recur.
Before installing any software, ask yourself the question: "Am I sure I know how to uninstall this without having to wipe the volume again?" If the answer is "no," stop.
Never install any third-party software unless you know how to uninstall it.