Creating a generic method in C#

I am trying to combine a bunch of similar methods into a generic method. I have several methods that return the value of a querystring, or null if that querystring does not exist or is not in the correct format. This would be easy enough if all the types were natively nullable, but I have to use the nullable generic type for integers and dates.

Here's what I have now. However, it will pass back a 0 if a numeric value is invalid, and that unfortunately is a valid value in my scenarios. Can somebody help me out? Thanks!

public static T GetQueryString<T>(string key) where T : IConvertible
{
    T result = default(T);

    if (String.IsNullOrEmpty(HttpContext.Current.Request.QueryString[key]) == false)
    {
        string value = HttpContext.Current.Request.QueryString[key];

        try
        {
            result = (T)Convert.ChangeType(value, typeof(T));  
        }
        catch
        {
            //Could not convert.  Pass back default value...
            result = default(T);
        }
    }

    return result;
}