As the gear and flaps were retracted after takeoff, the #1 engine low fuel pressure warning light illuminated. At about 400' AGL, a "loud bang" was heard followed by a #1 engine fire warning indication. The engine was shut down and both fire extinguishing bottles were discharged. The flightcrew extended the landing gear by using the alternate system and made a no-flap emergency landing. They used emergency brakes, but directional control was lost and the aircraft exited the side of the runway and stopped with the fire extinguished. An exam of the #1 engine area revealed a failed low fuel pressure warning switch snubber and fire damage to the engine, nacelle, and wheelwell. There was evidence that during installation, the low fuel pressure warning switch snubber was torsionally deformed, then fatigue and subsequent failure occurred. Gaps in the firewall allowed leaking fuel (spray) to enter the hot section and ignite. This resulted in an explosion and fire. Fire propagation resulted in burned wires to the #1 standby hydraulic pump and a ruptured #2 system hydraulic line.