New computer here, XP Home installed - plugged into the LAN and can ping
and be pinged but cannot get onto internet (neither via web browser,
ping etc.) The firewall (running on a Linux server) doesn't restrict the
IP address as far as I can see. Other machines on the netwrok are
accessing internet without any problems.

Is there some setting in XP Home one needs to tick in order to be
allowed internet access? I am using the default user which has
Administrator privileges.

Check the DHCP settings (under properties of the TCP/IP which can be found
in the network connection properties).

The server either needs to be able to give your computer an IP address
(dynamic) or you need to assign one yourself. The latter case sometimes
requires you to tell the server what IP you've assigned your PC. This all
depends on this Linux firewall system though, and I'm stabbing in the dark a
bit I'm afraid.

Failing that, are the proxy settings correct or missing?

David