I think that the very first time that you plug in you iphone to your computer a pop up will ask if you want it to always start up. If you just exited out then it prob wont start up. the good thing is that once you actualy get to the itunes account then you go to the devices section and make it automaticaly start up. If it doesnt work, im sorry im not a big computer person and this all is from experience.
You can change that my clicking the "open iTunes when device is plugged in" (or something along those lines). When your iPhone is plugged in, click the device on iTunes and on the general tab, near the bottom you will find some options to choose. :)