Better don't try halogen-lamps, they'll get incredible hot caged in your cabinet.
There are AC-filters out there which might cost about $10 -sorry, don't know how you call them in english, but I guess they would be worth a try, especially as your UPS helped, too. At least they are much cheaper.
Probable your kitchen-lamp only produces noise and gives it back to your powercircuits. Using a different circuit might help, too. Is it an old house? They tend more to have such problems - I live in an old house, too. Luckily it all seems to work, but kitchen, living-room and bedroom are all on the same circuit here which really sucks.