Happy New Year, Pete!
I'm also running Jeppesen FliteStar 9.3.0, and I installed the FstarRC 1.86 along with the FstarRC 2.00 update from above. I've verified that everything is present in the FliteStar directory. I'm experiencing the exact same problem. I'm running Windows 32-bit Vista. Not sure if that makes a difference.
Here's the entire contents of the FstarRC.log file with Log=debug set, so I'm not sure if zipping & emailing the file to you is really necessary:
0 ********* FstarRC, Version 2.00 by Pete Dowson *********
0 Sending RC plans to: C:\Jeppesen\FliteStar\
30 Error: no Base for for MFC42.dll
30 Error: couldn't hook DrawTextA
30 Error: no Base for for MFC42.dll
30 Error: couldn't hook DeleteDC
Is it some kind of path problem that could be fixed by setting an environment variable ?