Resolution:
The 3903 error translates to "The ROLLBACK TRANSACTION request has no corresponding BEGIN TRANSACTION."

This error will show up in the InConcert debug log as:
09:10:38 (wrkr) 00000d98 t00000820: debug: RPC done: 001032 Severity: 3 Time: 0.140 Queued: 0 Undefined status code 3903 for DBMS facility.

The API showing the error will vary!

In BWC logs it will show up as:

2007 Aug 03 11:19:27:740 GMT +2 BW.PRUEBA-Lanzamiento-JMS-Prueba-JMSProcess Error [WF-Plugin] BW-WF-100015 Workflow server error. Workflow server error. [ERROR/DBMS/3903]
    at com.tibco.workflow.plugin.errors.WfExceptionHelper.throwServerException(Unknown Source)
    at com.tibco.workflow.plugin.activities.WfPluginCreateJobActivity.eval(Unknown Source)
    at com.tibco.pe.plugin.Activity.eval (Activity.java:209)
    at com.tibco.pe.core.TaskImpl.eval(TaskImpl.java:540)
    at com.tibco.pe.core.Job.a(Job.java:712)
    at com.tibco.pe.core.Job.k(Job.java:502)
    at com.tibco.pe.core.JobDispatcher$JobCourier.a (JobDispatcher.java:249)
    at com.tibco.pe.core.JobDispatcher$JobCourier.run(JobDispatcher.java:200)
<?xml version="1.0" encoding="UTF-8"?>

NOTA BENA: The API at the top will differ.  It can show on any API which writes to the database.

Look at the IC status.log for other DBMS errors.  In this case the errors in the status log had the same time stamp as the 3903 errors in the debug log. For example, 2007 Aug 07 09:10:38:000 GMT +0200 WorkflowServer Error 3 5 1105 3480 2 129 129 0 Worker Undefined status code 1105 for DBMS facility.

The 1105 error for MS SQL server is:

"Could not allocate space for object '%.*ls' in database '%.*ls' because the '%.*ls' filegroup is full.

Explanation
The specified filegroup has run out of free space.

Action
To gain more space, you can free disk space on any disk drive containing a file in the full filegroup, allowing files in the group to grow. Or you can gain space using a data file with the specified database."

Note in this case all the status logs errors matched the debug 3903 errors date times.  Adding more data fixed the problem.

The second cause of this problem is manually running the IC upgrade scripts but not first doing  drop_procs.ddl and install_mssql.dml.  The stored procedures must also be dropped.

Causes of DBMS error 3903 with MS SQL servers