There are a lot of things that could go wrong, and a lot of tools to help us find out why it has. If you're familiar with the toolbox, including tools such as tcpdump, strace, ltrace, and pmap, you should be able to resolve most Zabbix problems.
As it would be quite out of scope, we won't discuss general Linux or Unix debugging here. Of course, there's still a lot of Zabbix-specific things that could go wrong. You might want to check out the Zabbix troubleshooting page on the wiki: http://zabbix.org/wiki/Troubleshooting. If that doesn't help, make sure to check the community and commercial support options from your local Zabbix partner or Zabbix SIA. We will discuss options, such as the Zabbix IRC channel, in Appendix B, Being Part of the Community.