Clone the current hard disk onto another one. Remove the current drive and put the cloned drive into the PC. If all went well, your system should boot up without any issues. Windows usually doesn't complain if the only hardware change in the whole computer is the hard disk.
The problematic drive can now be coupled to another PC that uses the tool MHDD for a really thorough check. This check can take hours, depending on the storage capacity of the disk, but you will have a much better understanding of what is wrong on your disk and where (on the surface(s)) these occur.
If these errors occur close to the beginning of the disk or at the end, you can use the MHDD tool to re-adjust the size of the disk, so it will be impossible for any operating system to access such a bad section ever again. The reduced disk can likely be re-used this way. Still, if you reduce the capacity of the disk, you will lose all the content of that disk, yes or yes.
CHKDSK is a tool that makes Windows work with a bad disk. CHKDSK manages/repairs content that has been malformed or misplaced, mainly by misused computers. That part of the concept "disk repair" CHKDSK does well. However, when the hard disk itself has actual issues, CHKDSK doesn't do so well. In those cases you'd better use proper tools like MHDD to investigate and optionally manage the problems on the disk. MHDD has a steep learning curve and can be dangerous in untrained hands.