is it cheaper to get another washing machine ?

When you press start one of the first things that happens is the door locks. The door lock also has contacts that feed back into the machine. Once the machine "sees" the door locked, it can get on with washing.

I wonder if there is either a problem with the electronics controlling the door lock ("all the lights come on") or with the door lock and / or the switch inside it ( "then all go off and it wont work")

If its the door lock, these are cheap enough and (relatively) easy to change. If its the board, then it still easy enough to change but may cost more.

Spares are listed here:

http://www.4lg.co.uk/washing-machine/wd-10130f/catalogue.pl?path=622102&model_ref=8251190

http://www.espares.co.uk/search/mo384806pt1980/washing-machines/pcbs-and-modules/lg/wm10130f

http://www.buyspares.co.uk/washing-machine/wm10130f/catalogue.pl?shop=lg&path=111341&model_ref=49209

XXX
June 2016

Well there is power because the lights come on.

If you own the property then you own the machine and can do as you please. A repair is likely to cost less than a new machine so it will be cheaper - will it be a sensible thing to do is another matter - how old is the broken machine?

If you rent the property then the machine is the responsibility of the landlord and you should not mess with it.

Good Luck...
June 2016