I can't seem to separate pitches. If there are 2 flat notes in a row, for example, I raise the first pitch. Then I raise the next pitch and it pulls the note I just put in the proper pitch back down again. This is with the pitch grid set to "no snap".
 
I've looked at tuturials but the tutorials always seem to use a toolbox that I can't access.
 
The tool bar has only 3 tools, the main tool, scroll tool and zoom tool.
 
If I right click in the edit area, which is supposed to open a toolbox, all I get is: select all, delete, paste, copy, cut.
 
Any ideas?

Are you hitting the Alt key when you drag the note?

Can you post a screen capture of what you're seeing in Melodyne?   I don't have Essentials, but what you're describing should be the same in all versions. 
 

Paul G
Are you hitting the Alt key when you drag the note?

Yes. It doesn't seem to make any difference.

This is the toolbox shown in all the tutorials as seen in the link "Melodyne in Cakewalk Sonar X3 with ARA"
http://helpcenter.celemony.com/essential2/en/singeltrack_daw_sonar.html#Changes-to-audio-clips-that-Melodyne-follows-automatically

I've never used that tool before, but it looks like it simply bypasses all pitch correction so you can do an AB comparison between the original and edited versions.   It sure sounds useful...  Thanks for posting that! 
 
Going back to the OP...   in the first image you have some active blobs.    If you click and drag that first Eb blob (fourth from the end) up or down, are you saying that the F blob next to it also shifts?  

Part one of the mystery is solved. Even though the Celemony link above says "essential2" on the URL (because I specifically used 'essential' in the search terms), what they show is not the Essential version, which only has the basic tools, as seen below.
 
Part two of the mystery is how to separate pitches so that I can move 2 pitches in a row higher without having the first one automatically lowered when I raise the second one or vice versa.
 
 

stevec
I've never used that tool before, but it looks like it simply bypasses all pitch correction so you can do an AB comparison between the original and edited versions.   It sure sounds useful...  Thanks for posting that! 
 
Going back to the OP...   in the first image you have some active blobs.    If you click and drag that first Eb blob (fourth from the end) up or down, are you saying that the F blob next to it also shifts?  

Yes, in the opposite direction. So if I raise the pitch in the 1st blob (love that term) and then raise the pitch of the 2nd blob, raising the pitch of the second blob to where I want it automatically lowers the pitch of the 1st blob to where I don't want it.
 
I'll do some more research. The frustrating thing is that most of the tutorials use the full tool kit. I hate spending hours using all kinds of creative search terms trying to get a plugin to do its most basic function. I was hoping someone here had more experience with Melodyne Essential, but I guess I'm on my own on this one.

The 1st blob could still be selected.  Try to click an open area then click the second blob to move it.  Tell us if that works?