Lights wont turn on and the yellow wrench light in on
your battery may be dead but I suppose you would have mentioned that, I would think it is a fuse or relay.
A service (wrench) light indicates BCM (body computer) code. It's like a "check engine light" for the rest of the car. Since your lights won't turn on, it's probably best to take it to a repair shop to get the codes read. Parts store scanners won't read it.
Search Chevrolet Cavalier Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Chevrolet Cavalier Experts