iphone 5c doesnt switch on and displays apple logo with writing on the top of screen

Have you tried restoring the software in DFU mode?

Turn your device off and connect your cable to the computer, but not the device just yet. Start up iTunes. Now, hold down the home button on your device and plug it in to the cable - don't let go of the button until iTunes tells you it's detected a device in recovery mode. Now you can restore to factory settings.

Try it more than once if it doesn't work the first time.