GU 5.3 MR16 Lamp probably 12v. Possible that the transformer is dead, they normally pack in due to excessive heat from the halogen lamp. Are you installing LED lamps?
Transformer should pretty easy to change for someone with basic diy skills but if your unsure call in a spark.
Just got halogen bulbs to replace them for now, will look into LED lights later (once i've used the halogen bulbs probably, these things are bloody expensive!!)
Next silly question, is the transformer in the little white plug we can see or is it further up in the attic?