You likely have version 1.14B whereas you need to have version 1.14D to access Classic Battle.Net.
You can patch your Diablo II LoD manually… simply copy the appropriate link below and paste it in a new tab in your browser. It will download the patch… normally in the “Downloads” folder and run it from there. You may want to save the patch somewhere on your PC in case you need to do this again.
Diablo II: Lord of Destruction - Patch 1.14D download links
PC version: http://ftp.blizzard.com/pub/diablo2exp/patches/PC/LODPatch_114d.exe
Mac version: http://ftp.blizzard.com/pub/diablo2exp/patches/Mac/LOD_Patcher_114d.app.zip
For future reference, there is a forum for Diablo II LoD support here: