leak from somewhere?

just put my house up for sale and guess what - the roof leaks.
i have a slate roof, which if i could afford it i should get renewed. but times are hard.
on the gutter edging there is a 4-6" black band tucked half way under the tiles, is this some sort of wind breaker?
i have discovered a wet patch on the wall at high level just below my guttering and wondered wether the fact some of this banding has gone could have something to do with the wet patch?
cheers and will acknowledge any responses