No. The 834G contains a reasonable home firewall, so you don't need Zone Alarm (but see below). However, it isn't a substitute for anti-virus or anti-spyware software.
You may wish to continue running Zone Alarm, even with the 834G, as it tells you when software that you may not know about (i.e. malware) is trying to connect to the internet from your PC - the 834G only blocks inbound requests. I'm using an 834G, but I've kept ZA for just this reason.