Shimano Hub LED lights working sporadically My Shimano hub lights are not working correctly.  All help greatly appreciated.  First time I've had a bike with lights like this.

Specifically, the rear works all the time.  But the front is basically out of action.

It worked on the way to an appointment, then on the way back it didn't.  I accidentally pulled the cable out of the plastic housing when I tried to rectify it (in the rain in the dark...) and so no lights at all on the way home.

The next day I reconnected the copper wire in the plastic contecter and the rear worked, but not the front.  Strangely it decided to come on after about 2km riding, on the way home - and repeated this pattern for the next three days.  Start the day dead, then come back to life after the journey home, just as I turn into my street.  But now it's even stopped doing that.

So...  Is the front simply "not charged", is that even possible, and if so, can I recharge it with a battery or something?

Or, as I read on an other thread, have I reconnected the cables in the wrong order and it's now shorting?

Or, something else?

Thanks for the help folks.
If I understand you, you have a hub dynamo that powers lights in the front and in the rear.  You don't make it clear whether you have a battery or not; if the lights stayed on after a minute or so (when everything worked properly) when the bike wasn't moving, then you have a battery.  If the lights fade and die a minute or so after you come to a stop, and then work again when you get rolling again, then you don't have a battery.  It's very unlikely that you have a battery next to each light, because that would make the system more expensive for very little benefit.

Your problem is most likely a loose connection between the light and the power source.  If you have a battery, then the battery is the power source; if you don't have a battery, then the power source is the hub dynamo.  An electronics technician would look at each connection between the light and the power source.  You could have a loose contact, or a corroded contact.  If the contacts are corroded, you can often remove the corrosion temporarily with a rubber eraser, a piece of fine-grained sandpaper, or an emery board that ladies use to file their nails; try the gentlest options first, because if you remove the metal plating on the contact, then the contact will corrode again very quickly.

Corrosion is often caused by moisture getting into the contacts; if the connector has a gasket, then check to see if the gasket is sealing.  If the connector is supposed to keep water out, but doesn't any more, then the usual fix is to replace the entire connector, which takes electronics repair expertise.  If your lights are several years old, then corrosion could have happened naturally.

Good luck finding and fixing the problem.  If you can't fix it, your LBS or an electronics repair shop can probably do the job.