Problems after farm restore

I had to do a topology change for a Microsoft SharePoint Server 2007 installation. The MOSS 2007 installation was currently on one physical server. The change implied splitting off the Database Server to another physical server, and keeping the original physical server as Web-Front End Server and Application Server. So I started a set of taks: I performed a farm level backup using the backup utility in SharePoint Central Administration. I ran the SharePoint Products and Technologies Configuration Wizard to disconnect the server from the configuration database. I ran the Wizard again to create a new SharePoint farm. I launched the Office SharePoint Services Search and Windows SharePoint Services Search services. I restored the farm backup. All of which went pretty well, till I started doing some test: I ran into several problems.