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