From over the pond in the UK. My 06 GT had this problem at the weekend, similar symptons what have been discussed on this thread and the other thread linked to this.
What I noticed when I turned ignition on is that there was power within the car but not enough to start. I had the sound coming from the shaker cd player similar to a cd shuffle for about two minutes .
I managed to get a jump start and go for a 20-30 mile drive, went out again on Sumday and everything was ok. I will try to arrange a test on the battery.
B.t.w at present I have only been driving the car at weekends so sounds common to other posters on here.
Great forum.
