Q: how can i back up my iphone4s

If I read your description correctly and the phone does not work AND there is no backup, on iTunes or on iCloud, then there is nothing to restore from. Your data is gone and you might be able to set the phone up as a new, blank, device. If it is undamaged.

More details of your plight may help in understanding your problem.

Bijupalakkandi wrote:

 

I think my phone is gone n itune mode ....

IF you see the iTunes logo and the USB cable on the screen, your phone has gone into recovery mode. You will have to restore the phone using iTunes on a computer.

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

And though this might not be what you wanted to read, but if the phone is in Recovery Mode, the contents are toast. No way to save. Only possibility is from a suitable backup done previously.