If you switch on your psp console after a long period of time and the psp will not turn on, the battery pack inside the psp is dead. The reason why the battery pack is dead is because it has no electrical charge remaining on it in order to power on the psp console.
To resolve this problem, you will have to use a psp home, car or usb charger to charge up the dead battery pack. When a battery pack is stud up for a long time, the battery cells start to get weak, so it may take longer to charge it up than normal. If you notice that the dead psp battery pack is not charging up because the orange charging led indicator on the psp doesnt light up, simply unplug the charger for 5 seconds and reinsert it back in, this will recondition the cells in the battery pack.