I know I have posted this before but I am asking my friends to take one more look.  I cannot believe there isn't a simple solution I am missing and this is a huge workflow issue that more than triples the time I need to finish a project.
 

1. When I click to enter a note on the staff, it never ends up on the grid.  Using 120 ticks per beat and trying to paste an 1/8 note at 01:02:60, for example, the note will end up at 01:02:43, or 01:02:78.  It doesn't matter what type of note or what beat, it ends up on an odd tick number and I have to go back and quantize.
2. Similarly, when copying, cutting, or pasting, dragging along the timeline doesn't snap to an measures or beats.

Since this suddenly stopped working one day, I seriously doubt the Sonar code suddenly went bad.  It is almost as thought I accidentally hit some kind of shortcut key or misclicked an icon and disabled Snap\.
 
Event Draw duration is set correctly. Snap to Grid is on.

sounds a little like a snap to zero crossing issue. you say its using midi ?
 

This is MIDI, correct.
 
It may affect audio clips but I don't know because I usually pasted them at explicit clock times.

If it helps things make sense, I just turned Audio Zero Crossings off and it didn't change things.

Is there some place else I should look?

Puzzling.   For me, and you know I'm not by any means a sonar fan, the snap works fine.   
 
For entry of notes in the PRV window, there are two places where snap can be enabled: globally, and then over-riding the global setting, each PRV window has its own setting ... then in Preferences, Snap, there's a mystical 'snap intensity' setting ... Never been quite sure what that does, but I set it at 'light'.   And then another mystical 'Magnetic test' setting:  also, for me, at light.   And then, turn OFF the 'snap to nearest audio zero crossings' -- perhaps this is your issue? 
 
You can't get to the 'Snap to Grid' preferences in an empty project, afaik, you must have an actual project loaded, before setting these values. 
 
Then when it comes to cut and paste, I'd strongly recommend getting used to 'paste by time' AND looking carefully at how the "selection range" is actually set:  MANY many weird and bad accidents happen by thinking you've selected one time range and actually a slightly different time range has been secretly slipped in by Sonar.