I believe Indy 9 came with Delphi 6 and Indy 10 does come with Delphi 2007 so the problem appears to be the differences between Indy 9 and Indy 10. Unfortunately, Indy 10 was not always backwards compatible.
Here is a brief overview of some of these changes Object Hierarchy Changes in Indy 10
The interesting part is you say the Net client connects fine...assumedly with the unmodified version of your server simply recompiled with Delphi 2007? If so then it sounds like you may have Indy 10 already installed to build your Delphi 6 system...