Error 16 can be caused by a few factors. The simplest being that the motherboard and HDD between them have no time reference. This could be as simple as needing to add the time to the HDD and by moving the HDD over to a hardmodded console with the time still stored. A Hardmodded Xbox with XBMC4Gamers for example has a clock that will drag the time from having the Xbox connected to the internet.
However it could also be caused by dashboard corruption, whereby, transferring the drive takes the error code with it. You move the hard drive, the other Xbox goes error 16 also. This is when its dashboard corruption. For this you would need to use FatXplorer to re-format the drive and attempt to re-add the original Microsoft files.
In the event you don't have a hardmodded xbox to transfer the files, it will be simplest to just assume the HDD is corrupted and maybe consider replacing the drive. If you can connect the HDD to your PC (and there are adaptors for both IDE and SATA that will work that connect to USB) you could run a drive scan to try to figure out if the drive is past its sell by date.