Being Windows vista it makes the solution much more difficult. The only real solution at this point is to backup all personal data and reinstall Vista.
With the amount of error stacks that is showing there is no way to repair the OS. Something has gone wrong.
So find out if they can get into Safe Mode to start backing up their personal data from their user folders, their website bookmarks and everything else that they need. I would wager to guess that the system doesnt have the media but a Recovery Partition.
If that is the case they can restore it to default after burning their data or transferring it to a external drive. Depending on the system that would require either F11 or F12 to boot to the Recovery Partition. from which they can restore it to factory settings and transfer their data back to the system.
From there i would suggest installing AVG or avast for a anti-virus solution. Both are free and very good. I would also suggest a check disk with the /r /f parameters. This is to ensure that there is no bad sectors on the drive and if there is some this will fix them or mark them as bad so that the OS doesnt use that area of the hard drive.
Sadly this is going to be the best possible solution that can be advised at this point. Vista doesnt have a repair feature and the inplace repair methods mentioned online are basically reinstalls anyways.