Integrated supply module, integrated voltage regulator module, many people call it different things but ultimately it regulates your voltage supply and when it starts to fail it can cause the problems your experiencing. It's located in with the DME electrics under the pollen filter.
Something else to take a quick look at is when you remove the pollen filters and the plastic panelling they sit on you'll find a hole in the wings both sides, ensure these are free of debris as they are drains and can cause all sorts of problems if they get clogged, there's also drains under the electrics box itself and the brake master cylinder, make sure these are clear also.
The battery voltage is low, but should still crank. Check the voltage at the terminal under the hood, since the voltage goes from there to the starter. Make sure the connection there is tight. Has someone removed the valve cover lately on that side of the engine?
I thought I had responded to this but apparently not. I'm with Herb. IVM for sure. Had same symptoms which were getting quite frequent (twice in one week), never had a problem again since changing it last spring.
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