Have you more than one ignition button eg, hob and oven? Is there a clock? Our cooker (Cannon) has push-button ignition for the hob and automatic for the oven. If any of the other items are working the fuse must be OK.
Some models use a battery.
We had one a while ago, where the battery was located in the housing of the button itself. Try unscrewing the button. If there's a battery, it'll possibly be located in there .... watch out for the battery popping out though, as it'll be under pressure as there will be a spring in there.
If it's not battery operated, then it's possibly the switch itself that'll need replacing ...... I'm assuming you've checked the fuse(s).