2.0tdci mk2.5 No electrics, Alternator?

Hello, my first post looking for some advice please 

2010 mk2.5 focus 2.0tdci manual, 75k miles

Usully when its really cold or damp the Aux belt makes a slight squeal but it disappears when it heats up, 2 days ago my partner took the car to her mothers then about 1 mile to the local supermarket, when she tried to start the car it turned over but wouldn’t start, I thought it would be a flat battery and would only need a jumpstart but because of the weather I only managed to get down to try and start it today, I was surprised when it started without a jump, so I left it running for 5 minutes with everything else turned off, and tried to drive the car home, the belt stopped squealing but I then noticed a burning smell, then the ignition lights came on and the power steering stopped working so I pulled off the road and turned it off, now I have no electrics at all, I lifted the bonnet, the battery cables now look discoloured (white) Im unsure if this is just normal discolouration with age, the 1 year old battery and cables where cold to touch though, but the alternator and bottom of radiator felt extremely warm,  I started breakdown cover on monday so will call them out tomorrow and try to get it recovered home.

Do you think it will just need an alternator or do you think the wiring will be burned out too? Anyone had similar problems?As Im unemployed at the moment I hope to fix this myself, will it be easy enough to fix?

Any advice or guides would be greatly appreciated 

Thanks Andy