Here is an example I have made up now, the only special thing I had to
do is to provide a base URI to the parser context so that the relative
URI pointing to the schema could be resolved. Note that I didn't bother
to put a string literal with XML into the program but read the XML from
a file first to put it in a string then for the example:

using System;
using System.Xml;
using System.Xml.Schema;

public class Test2005042103 {
  static bool valid;

  public static void Main (string[] args) {
    string file = args.Length > 0 ? args[0] : @"test2005042102.xml";
    XmlDocument xmlDocument = new XmlDocument();
    xmlDocument.Load(file);

    // from here on dealing with string only
    string xmlMarkup = xmlDocument.OuterXml;

    NameTable nameTable = new NameTable();
    XmlNamespaceManager namespaceManager = new
XmlNamespaceManager(nameTable);
    XmlParserContext parserContext = new XmlParserContext(null,
namespaceManager, null, XmlSpace.None);
    parserContext.BaseURI = "file:///" + Environment.CurrentDirectory +
@"\";
    XmlValidatingReader xmlValidator = new
XmlValidatingReader(xmlMarkup, XmlNodeType.Document, parserContext);
    xmlValidator.ValidationEventHandler += new
ValidationEventHandler(ValidationHandler);

    valid = true;
    while (xmlValidator.Read()) {
      Console.WriteLine("Reading node with name {0}.", xmlValidator.Name);
    }
    Console.WriteLine("Document is {0}.", valid ? "valid" : "not valid");
  }

  public static void ValidationHandler (object sender,
ValidationEventArgs args) {
    Console.WriteLine("{0}: {1}", args.Severity, args.Message);
    if (args.Severity == XmlSeverityType.Error) {
      valid = false;
    }
  }

}

That example works fine for me here with .NET 1.1, the example XML
markup in the string is being pulled in node by node and validation
errors are reported.

I used an example XML

<?xml version="1.0" encoding="UTF-8"?>
<god
  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
  xsi:noNamespaceSchemaLocation="test2005042101Xsd.xml">
  <name>Kibo</name>
  <power>a42</power>
</god>

with schema

<?xml version="1.0" encoding="UTF-8"?>
<xs:schema
  xmlns:xs="http://www.w3.org/2001/XMLSchema"
  version="1.0">

<xs:element name="god">
  <xs:complexType>
    <xs:sequence>
      <xs:element name="name" type="xs:string" />
      <xs:element name="power" type="xs:integer" />
    </xs:sequence>
  </xs:complexType>
</xs:element>

</xs:schema>