Switch - cable - transformer - cable - lampholder - lamp
There will be a problem (open circuit) somewhere along this chain. It's a case of finding where it is. Sometimes to save time naughty installers just tighten the terminal screws down onto the insulation of the wire, cutting through it rather than stripping it off as they should. Check all terminal connections. If you have more than one transformer - swap them over to see if the fault moves.
When it's all fixed you will be very pleased but in a few weeks you'll probably be fault finding again - I threw my kitchen counter top halogens away 18 months ago and fitted small neon strip lights at £9 each - no failures so far - cheaper to run, cooler and a better light spread.
Peccavi
November 2009