Fan won't shut off w/remote.
Does the remote have a dedicated button for off/on lights, and then off/on fan?
I assume it used to work,,???
First, regardless, replace the batteries in the remote, even if they are new.
This will do two things, reset the remote and double check the remote is powerful enough to send a strong signal.
Do you have the original set up manual for the fan?
If this is not a new install, and it simply quit, get out the manual and perform the original setup.
Sometimes there are "modes" setup on the fan by how long the wall power switch is on or off, say on for 30 seconds puts it in test mode, or on/off in less than 30 seconds puts it in operational mode.
Not knowing what you have, I cannot say that you need either a new fan or new remote, I need more information about the entire situation.
write me at service @emrrepair.com
Will