Very slow to start processes or open applications
First: Make sure you have an up-to-date backup. 

Assuming no hard drive issues, this Sounds like Spotlight is having problems indexing. I have also seen slow app launching due to bad font caches. 

I assume that you have let the system run for a while so that Spotlight can have a chance to update its databases. This can take a while, although on a relatively current Mac with an SSD drive, it should not take more than a few hours. 

It is also possible that there are other cache's or background cleanup utilities that are not running properly. 

You can try Onyx. Be sure to download the correct version of Oxny for your version of Mac OS X. Oxny is a GUI wrapper for a wide variety of command line tools to deal with these types of issues. After you run Oxny, you can expect the first startup time to be MUCH slower because various databases, caches and the like need to be rebuilt. There after, it should be back to full speed.