Magnetic contact circuit
Try this: 







simulate this circuit &ndash; Schematic created using CircuitLab

The MOSFET switches the current to the LED strip (containing series resistors and LEDs). The top connection of the LED strip is + the bottom is -. When the reed switch is closed, the MOSFET gate is connected to the source, so it is turned 'off'. 

This circuit draws about 1mA from the battery when off (through the LED and R1), so it will slowly discharge the battery. You can increase R1 to 20 or 50K if that is an issue, but too high and you can damage Q1 due to slow switching. 

Edit: See buffered version that draws only 12uA in the off state. D3 should have a breakdown greater than the battery voltage but less than the rating of the 4049, so I've used a 13V zener.