My car has 90000 miles.
My car has a manual transmission.
P0531 is a refrigerant pressure fault in the AC system, unrelated to the "hesitant start" issue you describe. It can, however, affect proper auxiliary fan operation, important in hot driving conditions. Hesitant start scenarios have a couple of possibilities. If the problem is lack of cranking the engine over, the problem could be a worn ignition switch, starter solenoid or starter - due to burned contacts in any of these components. If the problem is a lack of fuel pressure (after sitting a while), the problem could be a failing fuel pressure regulator, or a weak fuel pump, fuel pump relay with burned contacts, or clogged fuel filter. Any of these faults would require the fuel pump to run longer (along with the starter) to develop enough fuel pressure to start the engine. To properly diagnose this issue, a certified YourMechanic technician can come to your location to perform a car is not starting inspection on your vehicle and suggest or perform any repairs.
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