Dead Island Side Quests Walkthrough: A Ray of Hope
This quest takes place in the lighthouse. Completing this quest will unlock the area of the lighthouse where you can find the Amplifier for the side quest "On the Air".
The fastest way to get to the lighthouse is to use the truck (assuming you have completed the Lazarus Rising sidequest, if not then now is a good time to do that). Track a quest that takes you to the light house such as "on the air" and follow the road. Run zombies over for some experience points.
When you get there, talk to Darvin inside who is standing in front of the door. He will send you to James. Use the door and go out on the balcony where James is standing. James will ask you to help people around the lighthouse so that you can set it up to signal for assistance. This is also part of the Knockin' on Heaven's door side quest.
Now go back and talk to Darvin. He will give you the "A Ray of Hope" quest. For this quest, you have to find the transformers to fix the power in the lighthouse. He promises to let you into the storage shed once you do that. You need to locate Marcus who was sent to repair the transformers. Marcus is in the Golden Bungalows area. Follow the radar (preferably in the truck) to get there.
Once you get to the Golden Bungalows area, you will find Marcus trapped inside a fence surrounded by zombies. Kill the zombies and free him. He will then ask you to get the other transformer back online.
Travel downwards, kill the zombies on the way, and enter the transformer room. Turn on all the power units by flipping the switches on so that the lights turn from red to green. Then go back to Marcus. He will thank you and give you your reward, and send you back to Darvin in the lighthouse. Once you talk to Darvin, you will complete the quest and gain access to the storage area in the lighthouse