Error Code 80010514 explained...
Originally posted by another user
The error code is actually one of two things, a) a faulty sector on the internal hard drive, or b) a faulty installation of software/firmware, both iterations actually coincide with eachother. If the hard drive suffers a faulty sector ( a section of damaged space on the drive that data may have been written to that no longer is readable), an installation may still be processed, and even work, but the error can cause some serious side effects, such as option b. If your PS3 has installed an item incorrectly, including firmware, it is in high risk of receiving this error.
Lets sum it all up, the error is not hardware related and is caused due to corruption of firmware. Restoring you PS3 will not roll back the firmware, and unfortunately will not fix the issue 9 times out of 10. If you are receiving this error, contact Sony for a replacement unit. Again I hope none of my readers have to see the dreaded 80010514 error and by following Gamerevolver.com’s simple steps your bound to prolongue the life of your PS3 indefinitely.
Sorry mate, there's some parts i haven't pasted, just the most relevant. So you might wanna click the link and read a little more for more info.