While my answer may not be fully relevant to the complete patent claim list - this particular claim introduced nothing new, even in 1999. Breaking it down and narrowing the prior art:
Claim 1: A system for onsite backup of internet-based data comprising:
a central computer;
a client computer;
a communications link between said central computer and the Internet;
a communications link between said client computer and the Internet;
This part is pretty straightforward. Client, server, network connection between. Any information stored on the Internet accessible server is, Internet based data.
at least one database containing a plurality of data records accessible by said central computer, each data record containing a client identification number;
Database "servers" that reached "client" computers over network connections existed well before 1999. A "client identification number" is not novel either, every database since the creation of databases uses such "user ids".
software executing on said central computer for receiving a data backup request from said client computer;
The term "software executing on said central computer" is vague and the ability for server based software to "receive requests from client computers" is not novel in itself, Apache webserver had done this since the Internet started.
software executing on said central computer for transmitting said data backup to said client computer for onsite backup of internet-based data on said client computer.
Ah. This is a reverse backup. The server based data is backed up on the CLIENT computer.
But - this was nothing new in 1999. From an old project we worked on in the '90s - may I present Sybase SQL Anywhere. Version 5 released in 1995 (Wiki) had remote replication. Remote replication allowed MANY client database computers to be updated with the exact data from the SERVER (central) database computer. Essentially, a backup copy - a remotely replicated database.
This is how it worked:
A central computer (database server) and one or more client computers were connected to the Internet via a communication link.
At least one database file that had many (or a plurality) of data records was stored on the central (server) computer. Databases identified each client computer with a "replication ID", which was their client identification number.
The replication management software executed on the database server (central) computer, which received the data replication (backup) request from the client computers.
The replication management software executed on the database server (central) computer which sent packets of data to connected clients, the data stored on its Internet based connection (Internet-based data). This replicated data allowed each client computer to maintain an exact copy of the central database (the backup).
The end. Hopefully, of this patent.
Edit: Here is the Sybase replication documentation dated 1997
Article on product in PC Mag Dec 19, 1995 Google Books
Article on product in InfoWorld magazine Dec 4, 1995 Google Books
Article on product in Computerworld Oct 7, 1996 Google Books