there would normally not be enough activity against the model database to cause log growth so something is running against the model database that probably should not be, you need to find out what that is.

If the full backup is still running it suggests the active part of the log is large and that is being backed up as well. I would be tempted to kill the backup and find out what is running against the model database.

Once you have that tidied up you can switch to simple then back to full or as it is SQL2000 run backup log with truncate_only. you probably want to keep model in full mode as other databases are created from it.