I am unable to use my sony k750i, display shows

you can try a different sim in your device or your sim in a different device. You can also try pulling the battery with the device stll powered on and then remove and reinsert the sim if that doesn't work then you can try this:
If your sim works in a different device (they have to have your same cell provider or an unlocked phone) then it is your phone and a phone like that is unfixable when that happens. call your 611 from your handset if you can or just call your cell phone provider and see if you can get a warranty exchange.

If a different sim works in your device ( you can borrow a friends or family member just as long as they have the same cell provider) if the sim works then you need to go get a new sim.
you can ether order it off the internet from your cell phone providers web site or you can go to a store.