The battery (9v) died on my 10 year old fan. With the new battery the light goes on by itself every few hours and sometimes the fan changes speed on it's own. The remote works fine when you push the buttons. No other remotes are used at the time this happens.

The battery and this phantom operation are likely not related. Try moving one dip switch in both the receiver and transmitter.

What make is the fan?

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More

It is a Hampton Bay. The remote has no dip switches just 4 fan buttons and one light button.

Please reply to the thread, rather than comment on the post.

The dip switches are inside the remote and inside the fan. Please read the document I linked above.

Open the battery compartment in the hand held remote, see the little dip switches now? Look for the identical bank of switches in the receiver inside the canopy.