Thanks for all the answers guys. I did finally manage to get through to an English speaking operator at LAN. It seems the local office did make a mistake which seemingly they couldn't be bothered to correct. There was no code anywhere on the cards I was given but LAN did find my booking on their system and provided me with the ticket code that I needed.

Just as an observation for others traveling from Quito, LAN do expect you to check-in online and this can only be done, obviously, with the ticket code. Also, they recommend I use a system like checkmytrip.net as it can sometimes provide information about changes to the airflight which can be confirmed with them afterwards. Glad I called them, could have been in trouble with that one. Thanks all.