I had the same problem with my HP Deskjet 970Cse which was quickly resolved by going to the below HP site and looking under the Issue: The carriage is stuck or makes a grinding noise. Note that the blinking lights displayed as: Resume Light Blinking Simultaneously AND Power Light Blinking Simultaneously.
1. Lift the top cover to the printer.
2. Turn the printer off and then on again.
3. Unplug the power cable from the back of the printer when the grinding noise starts.
4. Move the carriage towards the middle of the printer.
5. Take out the cartridges and close the top cover.
6. Plug the power cord to the back of the printer. Turn the printer on.
7. Open the top cover, reinstall the cartridges, and then close the top cover.
Hope this helps as it worked for me.