To answer the question you should ask, the forms will ask you to declare your immigration history over some timescale. Specifically it will ask you if you have been refused entry to some country, and it may ask for all times this has happened, or for all the times it has happened in a time period (for example the last ten years).
Answer completely the question you have been asked.
If it asks for cases in the last ten years, give all the cases in the last ten years. If it asks for all, give them all. Don't give ones outside the time period asked for, but give any that you are unsure about (for example you can't remember if the refusal happened 10 or 11 years ago). You can assume that the check will cover at least the time period you have been asked for. The fact that it was on a different passport makes absolutely no difference. They will be able to retrieve records on different passports.
Never omit information that they ask for.
If you put information from a long time ago, that may or may not affect the outcome. Something from a long time time ago probably won't make a difference. However if you don't give information they have specifically asked for, that will cause an immediate denial, and probably a ban on future applications.