Do you mean there is not power at either wire of the low pressure switch, or that there is power at one side but it is not passing through the switch?
Assuming this is the manual A/C system, the low pressure (clutch cycling) switch on the accumulator receives power from the engine control module on the green wire; the dark blue wire is the ground side of the circuit, and runs to the control assembly.
If there is no power on the green wire, then it is because the ECM has not commanded compressor operation.
The first thing to do to diagnose this type of fault is to connect a scan tool capable of displaying live engine data, and see what the scan tool displays as A/C system pressure. This will tell you whether to look at the control side of the system (ECM, switches, wiring) or the refrigeration/ pressure transducer side of the system for the source of the problem...