My question is how to fix the problem with a remote - The Hampton Bay Ceiling Fan Remote works for the fan perfectly but recently stopped working for the light fixture - will not turn on or off the lights? Do we need a new remote?

You might need to replace your remote (not uncommon). Before that, try and reset your dip switch and battery. Remove battery from remote, more a switch or two to a different position and then back to original setting. Replace the battery with a new one. (remember to return the dip switches to the original settings). If this didn't help, it is easy to check the wiring connections for the light kit. Making sure the connector is tight and the wires aren't severely kinked. Home Depot has remotes for Hampton Bay fans. Just set the dip switch to match the old one. Hope this was helpful.