Macs only work with the original install disks to reinstall the original OS - you can call Apple and by giving them the serial number, they'd be able to send you replacement disks (however, that would be expensive). And yes, you can probably upgrade; however, keep in mind that a machine with an older processor, and having slower and the minimum RAM needed, it will not be an optimal computing experience.
I believe a better idea would be to buy the retail Snow Leopard disk, and update that to its latest version 10.6.8. That was a solid OS which will run older software and run happily on less RAM. The disk is available here:
http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
As for Apple and a possible Apple ID - I do not have a direct contact; you'd need to write to their corporate address found on this page:
http://www.apple.com/contact/
From what I've read previously, they require extensive proof.