Yes we have had the same problem in the past.
Certain toilet cleaners are good for cleaning the sinks and taps, and do bring them up to a lovely shine.
However, if the cleaner has been poured over the sink, and left there for even 20 / 30 seconds or so, then it has done its job and cleaned the areas that were covered.....but not the areas that were not covered.
Before going out and spending money on the suggestions on page 3 of the forum, go back to this sink with the toilet cleaner. This time pour over the sink and immediately cover the whole sink area using sponge or cloth. Hopefully this will rectify the problem.....if it does help...BINGO!!...If not then its back to page 3 suggestions.
All the best
Tim
P.S It may well be an idea to buy one of those products incase my idea doesn't work, then at least you are there and can use it straight away (careful and in ventilation....don't want you to mix chemicals in small area and then keel over). If you do not need it you can take it back and get your money back!!