My shower doesn't turn on when I turn the diverter
It sounds like there is a problem with the diverter valve. When you turn on the hot and/or cold water valves they flow through the diverter valve on the way to the tub spout. When you turn the diverter valve, it redirects the flow up the pipe to the shower head.

When a diverter valve malfunctions, initial symptoms usually include partial diversion, where some water comes out of the tub spout and some comes out of the shower head, it is unusual for there to suddenly be "no water out of the shower head" like you describe.

Special tools are usually required, like a shower valve socket tool which reaches deep into the wall to facilitate removal. If you want to DIY you need to give more info and post pics. If you are not ambitious, call a plumber.