Technically machine certificates, are stored in the registry under the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SystemCertificates\My key. But you would have a hard time getting them out - the private keys (contained in the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SystemCertificates\My\Keys subkey) are encrypred with a machine-specific encryption key.
So your two options to get you there remain:
- ask the certificate authority which originally has provided your customer with the certificates to revoke the current ones and re-issue them based on a new certificate signing request
- pull a copy of the Windows server machine's disks and try to get it running in a virtual environment to export the certificates/keys
Personally, I would prefer option 1. as it is likely to involve the least effort.