Chain on overhead combo ceiling fan/light wouldn't pull for the light part. Tried one last time and then the chain broke. Is this something that easily fixed?

The pull chain switch is replaceable but try to get one from the same manufacturer or brand. What brand and model do you have?

You'll have to remove the light fitter assembly from the fan. The switch is screwed into the side of the fitter. If it is only an on-off light, you need to get a single pole switch. Match it up at HD, Lowe's or an electrical supplier. There should be 2 small wirenuts to remove, reconnect and it should work. Good luck but please turn off the power to the fan first!