So if I understand what you're saying, you're trying to import the file into a SQL 2000 database table using MS Access 97? Is that right?
The SQL db_datawriter permission grants write privileges to the tables in the database. Full access would probably mean the user is an owner or a sysadmin, which it doesn't sound like it is. Not a big deal. The db_datawriter should be enough.
One thing I'd try is to make a local copy of the SQL table in Access and try to import the file into the local table to see what happens. Since you can import a small slice of it, I'm wondering if there is at least one record the table doesn't like. If that were true, though, then you should get a different error message.
Have you tried to import the file directly into the SQL tables using Enterprise Manager? That's something else I'd consider trying.