Why is it that "No HTTP resource was found that matches the request URI" here?

Your problems have nothing to do with POST/GET but only with how you specify parameters in RouteAttribute. To ensure this, I added support for both verbs in my samples.

Let's go back to two very simple working examples.

[Route("api/deliveryitems/{anyString}")]
[HttpGet, HttpPost]
public HttpResponseMessage GetDeliveryItemsOne(string anyString)
{
    return Request.CreateResponse<string>(HttpStatusCode.OK, anyString);
}

And

[Route("api/deliveryitems")]
[HttpGet, HttpPost]
public HttpResponseMessage GetDeliveryItemsTwo(string anyString = "default")
{
    return Request.CreateResponse<string>(HttpStatusCode.OK, anyString);
}

The first sample says that the "anyString" is a path segment parameter (part of the URL).

First sample example URL is:

• localhost:xxx/api/deliveryItems/dkjd;dslkf;dfk;kkklm;oeop
  • returns "dkjd;dslkf;dfk;kkklm;oeop"

The second sample says that the "anyString" is a query string parameter (optional here since a default value has been provided, but you can make it non-optional by simply removing the default value).

Second sample examples URL are:

• localhost:xxx/api/deliveryItems?anyString=dkjd;dslkf;dfk;kkklm;oeop
  • returns "dkjd;dslkf;dfk;kkklm;oeop"
• localhost:xxx/api/deliveryItems
  • returns "default"

Of course, you can make it even more complex, like with this third sample:

[Route("api/deliveryitems")]
[HttpGet, HttpPost]
public HttpResponseMessage GetDeliveryItemsThree(string anyString, string anotherString = "anotherDefault")
{
    return Request.CreateResponse<string>(HttpStatusCode.OK, anyString + "||" + anotherString);
}

Third sample examples URL are:

• localhost:xxx/api/deliveryItems?anyString=dkjd;dslkf;dfk;kkklm;oeop
  • returns "dkjd;dslkf;dfk;kkklm;oeop||anotherDefault"
• localhost:xxx/api/deliveryItems
  • returns "No HTTP resource was found that matches the request URI ..." (parameter anyString is mandatory)
• localhost:xxx/api/deliveryItems?anotherString=bluberb&anyString=dkjd;dslkf;dfk;kkklm;oeop
  • returns "dkjd;dslkf;dfk;kkklm;oeop||bluberb"
  • note that the parameters have been reversed, which does not matter, this is not possible with "URL-style" of first example

When should you use path segment or query parameters? Some advice has already been given here: REST API Best practices: Where to put parameters?

Have you tried using the [FromUri] attribute when sending parameters over the query string.

Here is an example:

[HttpGet]
[Route("api/department/getndeptsfromid")]
public List<Department> GetNDepartmentsFromID([FromUri]int FirstId, [FromUri] int CountToFetch)
{
    return HHSService.GetNDepartmentsFromID(FirstId, CountToFetch);
}

Include this package at the top also, using System.Web.Http;

WebApiConfig.Register(GlobalConfiguration.Configuration); should be on top.