Q: error code 4013

hi

after half submerginf my iphone 5s( approx 8 weeks old!!!!!) in half a cup of coffee during  very busy school run.. i dried it as best as i could , then poppd it in rice for 48hrs... and  whne plugged in sayd connect to itunes so i do and the apple logo and then restore process starts, only says waiting for iphone for ags and then the connect to itunes appears again on my phone and error 4013 on itunes...arrrghhh! you cna see the water damage under my screen still tho after leaving it to dry it has diminished a tiny bit... any hel or advice befor i take a very costly trip to the apple store? i am in the uk so if any one could giv eme a idea of the cost to replace through apple? no insurance and this will invalidate the warrenty i know ( i dont think i tripped the watr sensors tho??!)

thanks