Hello,
After starting the service, it stops after about 1 minute.
Logs attached

Following step were just been done successfull:

Verifying Mailbox Access

(In the following steps, some examples are shown. Please replace the bold parts with the appropriate details of your environment.)

1. Open Internet Explorer and logon as the LOGbinder service account, to the mailbox via Outlook Web Access using the server name specified in LOGbinder for Exchange control panel, such as

   https://ex1.acme.com/owa

   You should see emails in the Inbox or in Deleted Items from Microsoft Exchange with subjects, such as “Administrator Audit Log Search …” and “Mailbox Audit Log Search …”

I can see the Audit Logs but it seems that LOGBinder can't retrieve those files.
Regards

It looks like the service account running LOGbinder for Exchange doesn't have access to check the inbox. The logs show this:
The account CORPTESTLAB2\logbinder was unable to retrieve items from the mailbox logbinder@labmail.TEST.com, error: Microsoft.Exchange.WebServices.Data.ServiceRequestException: The request failed. The remote server returned an error: (403) Forbidden.;

You said above that you were able to log in to OWA.  Was this using the service accounts credentials?

Yes, the same as user set on the Recipient field in the input section.

If you can login as the service account, CORPTESTLAB2\logbinder, to OWA and access the inbox then LOGbinder should be able to access the inbox.  But the error from Exchange is this "The account CORPTESTLAB2\logbinder was unable to retrieve items from the mailbox logbinder@labmail.TEST.com, error: Microsoft.Exchange.WebServices.Data.ServiceRequestException: The request failed. The remote server returned an error: (403) Forbidden."

Please note this error message is from Exchange, not LOGbinder.  LOGbinder is just passing the error it's receiving from Exchange and putting it in the LOGbinder logs.  

A google search showed two interesting results:
1. https://social.msdn.microsoft.com/Forums/office/en-US/b2adfb0b-1f5f-48ed-bc73-b47116c6360f/ews-connection-office365-systemnetwebexception-403-forbidden?forum=exchangesvrdevelopment

That page suggests looking at the trace logs in Exchange to see more details on the error and to find out exactly why Exchange is denying access.  The easiest way to do that is going to be enable the trace log function, replicate the error, and then find the matching timestamp between the errors in the logs and see what the trace log says around that time.

2.  https://social.technet.microsoft.com/Forums/exchange/de-DE/9beed320-8e5b-4768-b362-7ecffb736bd9/ews-failing-with-the-request-failed-the-remote-server-returned-an-error-403-forbidden?forum=exchangesvrdeploylegacy

This page lists a simple command that may need to be executed to fix the issue.  This guy was on Exchange 2010 like you and was getting the same 403 forbidden error when attempt to access EWS.

On this page (https://support.logbinder.com/LOGbinderforExchangeKB/50027/1-Installing-LOGbinder-for-Exchange) under Step 2 I'm assuming you've set all the necessary permissions, correct? 

Hello,

Sorry for the late answer. We found the problem; the SSL certificate was not installed in the exchange server, so logbinder user could not log on and retrieve the mails.

thank you