If you are able to connect to the mailbox through your exchange mail then you should be able to do the same in EWS.
Create a service (ExchangeService) where you login with your exchange credentials and then use that service to connect to the mailbox
Mailbox mb = new Mailbox("processmailbox@domain.com");
FolderId fid = new FolderId(WellKnownFolderName.Inbox, mb);
ItemView view = new ItemView(100);
//use your service to get 100 mails from the mailbox
var findResults = service.FindItems(fid, view);
foreach (var item in findResults.Items)
{
var message = EmailMessage.Bind(service, item.Id, new PropertySet(BasePropertySet.FirstClassProperties, ItemSchema.Attachments));
}