There is nothing on the screen of the pedometer, what ever I press. Do they run on a battery and if so can it be replaced? There's no apparent place to fit a new battery!

Pedometers run on a battery, the type depends upon the exact make and model which you have failed to mention.

Many cheap giveaway pedometers are not designed to have the battery replaced but it's usually possible to carefully prise the case apart if it's not screwed together. Some are glued together in which case you'll need a razor saw: if you have to buy a razor saw then it's cheaper to just replace the pedometer. You'll often find that with cheap disposable pedometers that the batteries actually cost more than a complete new unit with batteries included.

More expensive pedometers will always have a clearly defined battery access point, even if it's just a matter of undoing a few screws to separate the casing..