I tried performing a Reinstall and also an Uninstall then Install from within CC.  I tried to uninstall and reinstall SONAR also.
 
For the SONAR reinstall, I had cleaned some registry settings based on some information that I found in the KB.  I can't say as there were any specific keys for Rapture that I deleted though.  Would have to go back and reread that article.
 
I do not know how to run Rapture in stand alone mode.  CC says "This product cannot be launched directly".  Is there a way to start it independent of SONAR?

The stand alone synth RaptureSession_64.exe should be in the folder with RaptureSession_64.dll
The default path is "C:\Program Files\Cakewalk\Vstplugins\Rapture Session"
 
On second though that won't work because you do not have an ASIO interface, I suppose you could try adding ASIO4All but before that we might try a clean install of Rapture Session. Give me a minute to look up the registry keys.

The steps to remove Rapture Session with the Command Center are

1. Run the uninstall for Rapture Session from the Command Center context menu. Only uninstall the Rapture Session line, there is no need to remove the content.
2. After running the uninstaller, remove Rapture Session's registry keys by doing the following:
   • Open the run prompt by holding down the Windows key on your keyboard and pressing "R"
   • In the Run Prompt, type in the following: regedit
   • Click [OK] and the Registry Editor will be opened
   • ***Back up your Registry before making any changes. You can do this by left clicking on "Computer" in the registry and then going to File | Export.
   • After backing up your Registry, delete the following registry keys:

HKEY_CURRENT_USER\Software\Cakewalk Music Software\Rapture Session
HKEY_LOCAL_MACHINE\Software\Cakewalk Music Software\Rapture Session
 
Use the command center to install Rapture Session again.

Just followed through these instructions and have ended up with the same result.  The first key, HKEY_CURRENT_USER, did not exist.  The second key did exist and I removed it before reinstalling Rapture Session.
 
Should I try ASIO4All?

Does the machine which works have the HKEY_CURRENT_USER key?
 

No.  It does not have the key under HKEY_CURRENT_USER either.

OK, it must be added on the fly when needed.
Does the machine which works use the internal sound chip or do you have a dedicated audio interface for it?

They're both using integrated Realtek audio devices.  The working machine is a Dell Precision laptop.  Both run Windows 10 Pro 64-bit.
 
One difference on the machine that isn't work is that it has a dedicated NVIDIA GeForce video card with available audio on HDMI.
 
 

SONAR performance is generally better when HDMI audio is disabled.

I disabled the NVIDIA sound devices in Device Manager as it would be very unlikely that I would use them.  The plugin crash continues to occur.
 
Are there any log files present at which I could take a look?