My version of Composite 2013 never did start. It always gave me a Runtime Error at startup:

So I removed it and installed Composite 2013 SP1. That version silently failed: in fact, I wasn’t sure it was even running until I used Process Monitor to watch composite.exe. Process Monitor showed me that Composite was writing log files in %LOCALAPPDATA%\Temp\toxik\logs, and I found this in the stdout.log:
Exception encountered: Cannot determine a product license to use.
This suggested to me that I needed to set the environment variable ADSK_COMPOSITE_LICENSE to Softimage, and that did the trick (when I checked, that environment variable was set to 3DSMAXDESIGN, and that’s why Composite was silently failing).
As a bonus, I also found the Composite Licensing log file %LOCALAPPDATA%\Temp\toxik\adlm.Composite.2013.log. The log entries make me think that my Runtime Error was caused by a Product Information (PIT) file problem. That’s why installing Composite 2013 SP1 fixed the problem.
584 2012/07/06 11:19:44 Reason=Fatal error
584 2012/07/06 11:19:44 ComputerName=MTL2UA0150CWY
584 2012/07/06 11:19:44 OS=6.1.7600.
584 2012/07/06 11:19:44 File=AdlmIntLicense.cpp,Line=584
584 2012/07/06 11:19:44 VendorID=6 [ADLMPIT]
584 2012/07/06 11:19:44 VendorError=12 [The root information in Product Information Table XML file is missing]
584 2012/07/06 11:19:44 Reason=Fatal error
584 2012/07/06 11:19:44 ComputerName=MTL2UA0150CWY
584 2012/07/06 11:19:44 OS=6.1.7600.
584 2012/07/06 11:19:44 File=AdlmIntLicense.cpp,Line=585
584 2012/07/06 11:19:44 AdlmIntError=25 [The product key was not found]
9448 2012/07/06 11:23:17 Reason=Fatal error
9448 2012/07/06 11:23:17 ComputerName=MTL2UA0150CWY
9448 2012/07/06 11:23:17 OS=6.1.7600.
9448 2012/07/06 11:23:17 File=AdlmIntLicense.cpp,Line=584
9448 2012/07/06 11:23:17 VendorID=6 [ADLMPIT]
9448 2012/07/06 11:23:17 VendorError=12 [The root information in Product Information Table XML file is missing]
9448 2012/07/06 11:23:18 Reason=Fatal error
9448 2012/07/06 11:23:18 ComputerName=MTL2UA0150CWY
9448 2012/07/06 11:23:18 OS=6.1.7600.
9448 2012/07/06 11:23:18 File=AdlmIntLicense.cpp,Line=585
9448 2012/07/06 11:23:18 AdlmIntError=25 [The product key was not found]
13860 2012/07/10 16:03:29 Reason=Fatal error
13860 2012/07/10 16:03:29 ComputerName=MTL2UA0150CWY
13860 2012/07/10 16:03:29 OS=6.1.7600.
13860 2012/07/10 16:03:29 File=AdlmIntLicense.cpp,Line=584
13860 2012/07/10 16:03:29 VendorID=6 [ADLMPIT]
13860 2012/07/10 16:03:29 VendorError=12 [The root information in Product Information Table XML file is missing]
13860 2012/07/10 16:03:29 Reason=Fatal error
13860 2012/07/10 16:03:29 ComputerName=MTL2UA0150CWY
13860 2012/07/10 16:03:29 OS=6.1.7600.
13860 2012/07/10 16:03:29 File=AdlmIntLicense.cpp,Line=585
13860 2012/07/10 16:03:29 AdlmIntError=25 [The product key was not found]
8368 2012/07/17 09:50:58 Reason=Fatal error
8368 2012/07/17 09:50:58 ComputerName=MTL2UA0150CWY
8368 2012/07/17 09:50:58 OS=6.1.7600.
8368 2012/07/17 09:50:58 File=AdlmIntLicense.cpp,Line=584
8368 2012/07/17 09:50:58 VendorID=6 [ADLMPIT]
8368 2012/07/17 09:50:58 VendorError=12 [The root information in Product Information Table XML file is missing]
8368 2012/07/17 09:50:58 Reason=Fatal error
8368 2012/07/17 09:50:58 ComputerName=MTL2UA0150CWY
8368 2012/07/17 09:50:58 OS=6.1.7600.
8368 2012/07/17 09:50:58 File=AdlmIntLicense.cpp,Line=585
8368 2012/07/17 09:50:58 AdlmIntError=25 [The product key was not found]