It will be hard to diagnose any electrical fault without a multimeter. I would suggest you get one as it will make the job a hell of a lot easier.
Something like thishttp://www.maplin.co.uk/domestic-multimeter-37279
There are obviously more expensive ones that have more bells and whistles, but for light, general use something like that is fine.
They are also essential to have for any kind of electrical/electronics work.