The fuel generator in Silent Hill 2 Remake is located in the basement of Brookhaven Hospital. You can get into the hospital basement using the key from the locker in the emergency room. The generator is initially turned off. To start it, you will need a fuel canister.
Where to find a canister and fuel for the generator
Empty canister
The red canister is located in Boiler Room 0.10, which can be accessed through Boiler Room 0.6. The empty canister is in the far corner on wooden pallets.
Fuel
The empty canister needs to be filled with fuel, so head to the linen warehouse, located opposite the Boiler Room. There you will find a box on wheels. It should be moved to the next room (laundry room) and placed under the window. There is a monster hiding in the laundry room, kill it before moving the box.
Stand on the box and climb over the window into the next room (warehouse). Use the red hose to fill the canister with fuel.
Once you have a full canister, exit the warehouse and go down the corridor to the left back to the generator. Fill it with fuel and start it using the red switch.
Once the generator starts, go back to the corridor and follow it to the end past the boiler rooms and the warehouse. At the end of the corridor, a monster, a cabinet with ammo and an iron grate will be waiting for you. After dealing with the monster, open the grate and go to the elevator. The elevator will take you to the second floor of the hospital, where the pump shotgun is located.
