Thank both of you for your help. LAV settings were indeed the culprit. My audio decoder button is still disabled, but DTS now plays.
Future readers with the same problem: DTS audio plays correctly when you ironically
uncheck the two DTS bitstreaming checkboxes in LAV Audio setup.
http://imgur.com/5OZfwsM
My copy of LAV is part of K-Lite Codec Pack.
If your setup is different, note that you can start the pictured configuration dialog with the following command in PowerShell or the command prompt:
C:\Windows\System32\rundll32.exe "C:\
PATH\TO\lavaudio.ax",OpenConfiguration