I'm not sure what the problem is here, All you need from the GOG version(or another install) are the "mp_bin.pk3", "pak0.pk3", "pak1.pk3", and "pak2.pk3" files that are in "etmain"(put them in the "etmain" folder for you ET legacy installation.)
Technically speaking you don't even need a separate installation as the ET Legacy Installer can download and extract all needed files.
If you didn't actually have the files though you wouldn't even be able to get to the main menu.
What you are describing sounds like one of a few problems:
1. You may be trying to join a server using PunkBuster and Pb doesn't work with ET Legacy(and I don't think many servers use it)
2. The server is using some other mod(maybe ETPro?) that is incompatible with ET Legacy.
3. You are trying to join a server with some other custom files(like 3rd party maps) and either you or the server doesn't have it set up to allow downloads. Check the "get missing files" and the "use http/ftp downloads" options in the "options/system" menu.