Hi Richard
It sounds to me like battery is coming to the end of its useful life. The excessive voltage drop when car is initially first started is dropping to such a low level is causing the power window switch to lose its memory setting and also for the immobiliser warning light to stay on. Once car has been started and turned off and restarted again battery has regained sufficient voltage to cause immobiliser warning light to extinguish.You can carry out a battery test-i.e a heavy discharge test to see if battery is still good but it does not always show up as it happened in my case, I have 2 Jazz, a 2006 1.4SE and a 2007 1.4 Sport and both batteries failed last year showing the same symptoms as yours did. Battery test did not show up any of the batteries as low or faulty (even the "window/magic eye" on the battery showed okay but after replacing the batteries car starts fine and no starting problems since then. One was replaced with the original Furukawa battery from Honda at £60 after discount and the other a Yuasa from a motor factor for £36 again after discount. Both batteries seems to be of equal quality,Yuasa is cheaper because its UK made,the other is imported (chinese made though)