eAccelerator works great on PHP 4.3.11 / Win32. I see roughly a 70-80% speedup in eZPublish page rendering with eAccelerator, down to about 0.1 seconds in total for the most complicated pages when caching and template compile are enabled.
There are versions (here is a link: http://rpmfind.net/linux/RPM/freshrpms/fedora/2/php-eaccelerator/php-eaccelerator-4.3.10_0.9.2a-0.1.fc2.fr.i386.html) that include support for 4.3.6 and up.
You REALLY do need to upgrade. Your box is at risk for gettin' hacked.