The TARDIS looked like an extra-tall plastic machine, hinged to open, much like a soda dispenser, but kept its essential police-box "texture". The Doctor and a companion were being abducted by a criminal group in the 1980s, but he had a plan.
It all hinged on simultaneous parallel worlds somehow combining - for example, a character with a brother in one world (under one set of circumstances) had a different brother in the other. One character was waiting to hear a particular song, which the Doctor sang into the history of the world.