You've been given a lot of good information, but ya, it might be time to take a deep breath and start from scratch. 
This: 
"Okay, I disconnected the midi track from the arp, muted the arps and redirected the midi to a synth. It still makes no sound. So I muted the midi track, unmuted another midi track and routed it to a synth. No sound and it was never hooked up to the arp. I brought up another song file and everything worked.
 
Any idea what shuts down all midi playback?     Does the synth play if you open its GUI and pre view , this works best if the synth has a little keyboard to use) if not the output of the synth might not be going to your MASTER output. 
 
Actually, my midi inputs and outputs to hardware synths seems to have gotten screwed up when I updated Sonar a few months ago. While fiddling around I rearranged the synths' inputs and outputs, and now none of them seem to work. " 
This seems to me the heart of the problem. updating Sonar will have nothing to do with this issue. Preferences remain the same unless YOU change them. 
 
I think this explains a lot of what is happening to you. My advice is to start fresh here and put things straight first otherwise nobody here will be able to figure this out as there are to many variables at play. 
 
Open a new project just to rule out weirdness in the one you were working on ( high probability) 
 
First go through your preferences and and make sure things like your MIDI devices are showing and checked. 
I think your looking in the wrong place,  the setting in Utilities you mentioned is I think for using Sonar as a live vst host and nothing to do with recording.   
Your midi inputs/ outputs are controlled in Preferences./ MIDI / Devices 
 
Now did you check the little icon in the taskbar lower right flashes when you play your keyboard? 
 
OK now insert a VST Soft synth and check " First synth audio output" when the GUI opens select a patch and test it using the GUI keyboard. 
Now insert a midi track and set the input to use your controller keyboard  and set it at OMNI.
Now set the output of the midi track to the VST  
You should hear the VST now, I'll wait to see if this works before carrying on.