Radio player turning on problem on Neon 2001 SE

I have a 2001 Dodge Neon SE. Some time ago the radio stop to work. When a
push the turn-on button, the radio station led begins to blinking (three or
four times), a “tick” sound is audible from the speakers each time the led
panel turn on/off, and then the radio turning off.
First time I though it was a battery problem because when a disconnected and
connect the battery, the radio became alive again. But if I touched the dial
button (for example: to raise the volume) the radio turned off.
A replace the battery for a new, one but the problem persist. Any idea? Thank
you in advance.