SONY

from sony support site "The error TURN THE POWER OFF AND ON AGAIN will be displayed if the lens assembly is not operating correctly. Ensure fresh batteries are installed or make sure they are fully charged and then try turning the camera off and then back on.

NOTE: If the error message still occurs, service may be required."

I think you can pass on checking the battery. obviously your lens mechanism is somewhat busted, and you'll have to get it repaired.
I'm sorry theres nothing I can tell you which is DIY.
Use your warranty if valid.

Good luck

The lens element is damaged internally and needs to be replaced as an entire unit. The camera runs through a "self check" each time it is powered up and it is detecting an error in the lens. Ship this unit to Sony in Laredo, TX. The warranty may not apply if they see there is impact damage to the lens. The flat rate repair charge will not apply here either due to physical damage to the lens element. be sure to request an estimate before the work is performed. Hope this helps you, we see this problem all the time with digital cameras that have lenses which extend during operation.

Joe Weibel
Custom Electronics
(customelectronics.org)