I think Runtime DriveImage XML could let you do this since it supports hot imaging/cloning. Meaning you could be able to clone your system drive while it is in use. I have tried it in XP machines before .
You can try to replace the optical drive or make a bootable USB windows 7 installation disk from the Windows 7.iso that you have and try to install Windows 7 on that PC from the bootable USB that you've made.(That is if the BIOS of this PC already supports booting from USB)
Yeah, you may need to install and use CrystalDiskInfo to check and verify your drives health status or SMART reports. And its also much safer if you do back up your data before the drive will fail though.