Check any stray earths around the battery area, I had this before on a mk4 gti 2.0 l but I lost all clocks,dash lights etc yet the car started and ran fine. Towed it back to the workshop and found a few earths had come off (iirc they go to a block below the battery tray). Cleaned some connectors up and renewed the eyelets and she was great. It had been crash damaged and this was after the lad had removed the battery to pull the leg hence I`m wondering if its the same thing.