IPhone – If the top button on the iphone 4 doesn’t work can I turn on the phone without connecting it to a charger

If you plug an iPhone into a charger it should power on. If it's on but frozen, you could connect to iTunes and reset/ wipe it, but that might lose some data depending on your backup situation and what is on the phone.

If it doesn't, then there is a hardware problem and you'll need to get that fixed or live with a faulty device.

Playing the Clock alarm sound requires the main application ARM processor/CPU to be running the OS and Clock app. When you "slide to power off", power to the main CPU, radios and audio amplifier is removed. So, although the iOS device keeps time (as long as the battery isn't completely dead yet), it can't run the Clock app to play any sound.

When you just "lock" the device (quickly tap the top button and the display turns off), the CPU still occasionally gets power (something like a few times per second), and the audio circuits can be powered and active (to allow background music, etc.), so alarms can go off in that state.