Office 365 Mailbox programatic access fails: The Autodiscover service couldn't be located.

Not sure if this is the correct place but here goes:

I have been given a mailbox and I have written a windows service to look into the mailbox and process email messages.

The mailbox is of the form: createlead@api.mydomain.com

I log in to office365 with this email address and the password and I can see the mailbox just fine.

I try to connect with code:

ExchangeService service = new ExchangeService(ExchangeVersion.Exchange2010_SP1);

Service.Credentials = new WebCredentials(username, password); //username as quoted above.

I get the following error:

Microsoft.Exchange.WebServices.Data.AutodiscoverLocalException: The Autodiscover service couldn't be located.
   at Microsoft.Exchange.WebServices.Autodiscover.AutodiscoverService.InternalGetLegacyUserSettings[TSettings](String emailAddress, List`1 redirectionEmailAddresses, Int32& currentHop)
   at Microsoft.Exchange.WebServices.Autodiscover.AutodiscoverService.GetLegacyUserSettings[TSettings](String emailAddress)
   at Microsoft.Exchange.WebServices.Autodiscover.AutodiscoverService.InternalGetLegacyUserSettings(String emailAddress, List`1 requestedSettings)
   at Microsoft.Exchange.WebServices.Autodiscover.AutodiscoverService.GetUserSettings(String userSmtpAddress, UserSettingName[] userSettingNames)
   at Microsoft.Exchange.WebServices.Data.ExchangeService.GetAutodiscoverUrl(String emailAddress, ExchangeVersion requestedServerVersion, AutodiscoverRedirectionUrlValidationCallback validateRedirectionUrlCallback)
   at Microsoft.Exchange.WebServices.Data.ExchangeService.AutodiscoverUrl(String emailAddress, AutodiscoverRedirectionUrlValidationCallback validateRedirectionUrlCallback)
   at LeadProcessor.Library.MailboxHelper.GetBinding(String Username, String Password) in C:\...\LeadProcessor\LeadProcessor.Library\MailboxHelper.cs:line 472
   at LeadProcessor.Library.MailboxHelper.GetEmailHelper(String Username, String Password) in C:\...\LeadProcessor\LeadProcessor.Library\MailboxHelper.cs:line 491
   at LeadProcessor.WindowsService.Service1.ProcessMailbox(Organisation Config)

I have tried the Remote Connectivity Analyser but can't work out which option I should be choosing (Office 365 General Tests? Single Sign On?)

Tried this and got error: The domain  isn't a federated domain.

Not sure if this is saying I am using the wrong option in the Remote Connectivity Analyser or if there is something wrong with the mailbox.

Can anyone help?