I use a solution of Caustic Soda to clean the chrome shelves of my cooker - it's very nasty stuff and can damage paintwork and any body parts it touches - it stings the hands and needs to be washed off immediately.
In your kitchen there will undoubtedly be spillages on the floor - splashes and drips of all sorts of stuff.
In your situation I might try a test area of Caustic Soda and a wire brush to remove any build up of dirt, fat and protective layers you may have applied. Let the solution of caustic soda do its work for an hour or so before scrubbing.
Long-term it may be wise to put no protective layer on the floor - dirt may get trodden into it - and to mop the floor on a daily basis to keep it clean.
I am not permitted to advise a new floor but Amtico is excellent.
Use google - select images - enter Amtico - be impressed.
Good luck...
Peccavi
March 2011