iMac not booting completely
My iMac does not book completely, I have repaired the hard drive using disk utility and also tried to reinstall the OS. Though I don’t have a back up for my files. How can I fix the problem without loosing my files
If it's not booting up properly, then something has gone wrong, repairing the hard drive in disk utility if there was something wrong with the drive, then there may have been some files that were corrupted by the drive failing. Really there isn't anything that the repair can do to repair files, it can basically mark sectors that are bad as bad so your computer will not try to read those sectors.
Basically, if you didn't do a backup and the files are corrupt which are causing your computer to be unable to boot, this is why I constantly tell people that they need to backup constantly because it isn't a matter of "if" you're going to have an issue, it's a matter of "when". It sounds like your hard drive had issues, things got messed up and now your OS is corrupt. That being said, you're only option to get it working again is to reinstall the OS. If you didn't backup your files, then your files that are on that drive, are not going to be readable by that computer if at all. You may need to take that drive somewhere to get the information off it before doing any more to it if it's imperative that you keep that information. Otherwise when you start the install, it's going to erase everything that is on that drive and you may not be able to retrieve them at all.