What is the advantage of using ASP.NET versus ASP for an application which will consume Web services?
In this case, it sounds like you want to build a Web site or portal that uses Web services to implement some of the underlying functionality, leaving the Web pages focused on presentation. For your Web pages to use Web services, you will need a toolkit in order to talk SOAP to the Web service. While Microsoft had a toolkit to do this from ASP, this implementation was very limited (for example, it was complicated to work with complex data types) and didn't have any direct support in Visual Studio. In contrast ASP.NET, together with Visual Studio.NET, provides a robust runtime engine together with a rich integrated environment for developing, testing and using Web services. Unless your Web services are very simplistic (and will stay that way forever!) I would recommend going with ASP.NET.
On the other hand, you can do some interesting things with manual coding (in either ASP or ASP.NET). For example, if you build your SOAP requests manually and send them using a raw HTTP connection, you can take the resulting data stream and directly convert it into HTML using an XSL-T stylesheet. The downside of this approach is that you can quickly hit a wall if the complexity of your page goes beyond what you can do in a single stylesheet (for example, if you need to invoke two Web services to generate the page content you could not use the stylesheet approach).