Hello XXXXXXXX,
Welcome to Just Answer.
Sorry to hear about your problem.
If you are sure that the bulbs are good, then the four lights were either not wired or more likely are controlled by remote control only. I have a similar Hampton Bay fan in my house that uses a remote to control two separate lights; there is no other way. There is a wall switch that controls the fan, and only the lights that were left on by the remote will come on with the wall switch. My guess is, you may need to find the remote or order a new one. One giveaway, that it uses a remote, is it will have a 12 inch wire coming off the top of the fan which is the antenna.
Home Depot is the exclusive seller of Hampton Bay products, so everything has to go thru Home Depot and they can order the remote for you; they are the only supplier of Hampton Bay. You can either visit your local store and order the part in the lighting/ fan department or you can call the parts department directly; Home Depot has a special phone number just for Hampton Bay replacement parts: 1-877-527-0313. Just have as much information about the fan as possible, like the name, model number, etc. to make it easier for them to locate the correct part.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
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Architect
Licensed Architect- 12 years, L.E.E.D. AP, Former Remodeling Contractor- 10 years