I believe your only problem is the web server's configuration. Each web-service's configuration (web.config file in my case, since i'm using IIS) should allow the management of the protocols allowed to access it: Get, Post, and/or Soap.
I've just tested my own web-service and it replies to GET requests from my browser... It also answers as expected to POST requests ( I adapted some code from https://web.archive.org/web/20210619192654/https://www.4guysfromrolla.com/articles/022410-1.aspx into the following snippet: )
Dim payload As Byte()
payload = Text.Encoding.ASCII.GetBytes("paramName=firstValue&p2=secondValue")
Dim webRequest As System.Net.HttpWebRequest
webRequest = System.Net.HttpWebRequest.Create("http://www.servername.com/DataService.asmx/GetVersion")
webRequest.Method = "POST"
webRequest.KeepAlive = False
webRequest.ContentType = "application/x-www-form-urlencoded"
webRequest.ContentLength = payload.Length
Dim reqStream As System.IO.Stream
reqStream = webRequest.GetRequestStream()
reqStream.Write(payload, 0, payload.Length)
reqStream.Close()
Dim webResponse As System.Net.HttpWebResponse
webResponse = webRequest.GetResponse()
Dim reader As System.IO.StreamReader
reader = New System.IO.StreamReader(webResponse.GetResponseStream())
Dim xmlDoc As System.Xml.XmlDocument
xmlDoc = New System.Xml.XmlDocument()
xmlDoc.LoadXml(reader.ReadToEnd())
Good luck.