Peter Behr pointed out that webmail wasn’t working. The problem was after logging in, (for me, in Safari) I’d get a can’t open page redirect.php error. (In Firefox, the page would just be blank.) I looked at some files on the shop computer, where webmail (squirrelmail) was still working ok and found some differences in the /etc/httpd/conf.d/php.conf file. The solution was to add the following to the php.conf on the hep computer.
AddType application/x-httpd-php .php
Restart the web browser and things started working.
I think this must be due to the different versions of php used by the different versions of redhat. The broken computer is running RHEL4 ES release 4 (server), while the working one is running RHEL4 WS release 4 (client).