Yes, Prof - just think like it's a bike! You'd immediately suspect connections from battery posts, then the battery itself fading. This is the classic time of year for them to feel the strain having heaters on, lights etc. They can have enough juice to run your electrics, but the juice required to turn the engine might not be there. You need to measure the batteries outputs under load/running etc. Either multimeter it, or just get a relatively cheap battery tester.
A 07 car, the earth's could be involved?