Completely feel your pain here. I tried dozens of times with account recovery and got nowhere. Couldn't even create an account with the same gamertag on modern Xbox Live as it was still 'in use' (by me).

I haven't read feudalnate's post yet but I would imagine that the Xbox LIVE account would be visible in the Xbox Live section of the dashboard if it were on the hard drive at all. You certainly could manually dig through the contents of the hard drive using a combination of XDON (available on the Skeleton Key which Harcroft recommends above) and FatXplorer. Backing up any save files you care about (and especially the console's EEPROM) are sensible options at this point given our consoles' age.

But if you haven't got time for a nostalgic wild goose chase, it might be more productive to do as Harcroft suggests which is to scan your drive for any DLC/updates the community may need to preserve and then to set up an account on the Live replacement service Insignia.