funcionar vs trabajar
In English a machine 'works' as well as a person. In Spanish, machines funcionan and people trabajan.
funcionar
To work (of machines, plans, systems) — to function properly.
El ascensor no funciona.
The lift isn't working.
A broken machine. Never 'no trabaja'.
Esa idea no va a funcionar.
That idea isn't going to work.
Plans and ideas can function too.
¿Cómo funciona esto?
How does this work?
A common question when learning a gadget.
trabajar
To work as a person — a job, effort, a task.
Trabajo en un banco.
I work at a bank.
Where you work. Trabajar en + place.
Trabaja de camarera.
She works as a waitress.
Trabajar de = to work as (a job). 'Trabajar como' also works.
Hoy no trabajo.
I'm not working today.
Days off. Also 'trabajo' = work or job.
Tricky bit
'Mi coche no trabaja' is understood but sounds like the car lacks a job. Always 'funciona'. For people, 'funcionar' is wrong unless you mean something like 'he's not functioning today'.