15 Passes of write zeros? I don't think even the most expensive deep level scanners in a lab would find the data. Since I think even 5 passes would already be impossible to recover something.
Hard drive prices will eventually fall down but not really that quick. Thinking that a 80GB hard drive 15 years ago cost as much as a 4TB drive today. :)
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 .
This trick might actually work on some older drives that still had low density platters. But is not totally recommended on todays earlier high density platter drives.
I'd probably suggest you to image the drive using ddrescue in Linux. Then it would be much easier for you to recover the files you wanted from the image you got.
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)