I really don't get why would you only want one user per pc. You might want to limit an account to a specific pc, but why would you want to do it the other way around?

Anyway, if a user installs a program, you could let that program check for the MAC address of the network card, the CPU Info and possibly other metrics, but none of which will be definitive, because a PC is not a single entity. Users can install another network card and/or CPU, add memory, get a new CPU etc etc etc. Ofcourse you could get them to re-register after making the changes, and update the database.

As for identifying users, your best bet would probably still be a username/password entry.