Finder crashes constantly
Observations

The file is found, but a symbol is not found. 

I sought information after the discussion in Ask Different Chat but found nothing conclusive. As the operating system misbehaviour is extraordinarily bad – both (a) for a new user and (b) in safe mode – I suspect a corrupt installation. 

As you also found a problem with archive and install without Apple's DVD, I wonder whether something troublesome has been done with 10.6.8 files that are hardware-specific and not good for the iMac10,1.

Advice

Reinstall the operating system. 

You don't have a DVD for installation, but your customer might obtain a replacement disc from Apple; or you or your customer can purchase the missing disc. 

Prior to reinstallation

Backup to separate media. 

Disk Utility can check the HFS Plus file system structure of a volume, but not media, so you might like to verify media before backup and installation.