Suzanne I'd hold off buying a cleaner, unless there's a pound shop near you where u can buy 1 for £1. The cleaner is like a cd with has little cleaning bristles. Your cdp has to be working for the cleaner to work as you put it in your machine just like a normal cd, it spins round and the bristles clean the cdp lens. As your player doesn't work and won't spin cds the cleaner will not work.
If it is a lens problem, which I doubt, you can clean the lens VERY carefully with a cotton wool pad SLIGHTLY wetted with distilled purewater, or failing that tapehead cleaning fluid or as a last resort neat Vodka [which is virtually neat alcohol].