Let us reverse Engineer it, I have come across these types of situations a lot time ago.
Here is the clue, you said you are able to execute the application and the same dll as exe right? Check what Date formatting is it being used there and one more advice is, go to the stored procedure because you are able to find the stored procedure using the SQL Profiler right? Try to execute the SP by passing the different Parameters and replicate the same error, then you would know what formats the SP is accepting and what formats the sp is giving the errors and why?
Then you can fix the issue in the Web Service to use the same format - what you are going through is similar what many have sometime back when everything moved from VB6 to .Net Framework - but its OK.
I do not have the VB6 dll source from my provider, so I have no way of getting the error.
I am attaching images of errors captured by SQL Profiler, but I don't think they can help.
The 1.png, 2.png and 3.png files are screenshots of the SQL profiler traces captured at Runtime, while the 1_Debug.png, 2_Debug.png and 3_Debug.png files are screenshots of the SQL profiler traces captured in Debug (so working).
Since the errors do not occur by calling the VB6 dll from VB6 or VB.NET applications, or by debugging my VB6 project which instantiates the external dll, I thought the problem lies in the process that hosts it.
All the messages seem to be complaining about the syntax of the SELECT clauses (assuming my innterpretation of the Italian is coorect), and suggesting that it has something to do with the Date values. I think the only way to resolve this is to talk to the owners of the DLL.
What Dave said might be correct too, since Service is to transport the Data it must be Serializable or Distributed that would be a problem but to know the real problem - try to replicate the issue on Stored Proc by passing different Date formats as I can guess you have only one source code that's exposed to you all other are either dlls or exes, which you can't reverse them into VB6 code back. So focus on one Source Code you may probably have or know that's SP and try to replicate the problem.
Checking the VB6 code with the developer, we have identified the point where the error occurs: it cannot return a path of the configuration file (from which it reads the formatting of the dates), and uses the Windows API "GetEnvironmentVariable" .
I'm trying to figure out if there is any incompatibility between WCF and the VB6 API calls.
If you're hosting the WCF service in IIS or a Windows Service, it will be running under a different profile. Unless the environment variable is set as a system variable, it will be specific to your user profile, and will not be available to the WCF code.