＞・Zabbixエージェントが動いているか

以下の通り、動いております。

# service zabbix-agent status
zabbix_agentd (pid 3189 3188 3187 3186 3185 3183) を実行中...

＞・Zabbixサーバから接続できるIPとポート番号でLISTENしているか

これはzabbix_agent.confにListenの指定をしないといけないということでしょうか？

参考までに、/etc/zabbix/zabbix_agent.conf の内容を載せます。

----------------------------- ここから -----------------------------
# This is a config file for Zabbix internet service daemon agent
# To get more information about Zabbix visit http://www.zabbix.com

### Option: Server
# IP address of Zabbix server
# Connections from other hosts will be denied
# If IPv6 support is enabled then '127.0.0.1', '::127.0.0.1', '::ffff:127.0.0.1' are treated equally.
#
# Mandatory: yes
# Default:
# Server=

Server=192.168.1.197（サーバIP）
Hostname=hogehoge（クライアントPC名）

############ ADVANCED PARAMETERS #################

### Option: Alias
#
# Mandatory: no
# Range:
# Default:

### Option: Timeout
# Spend no more than Timeout seconds on processing
#
# Mandatory: no
# Range: 1-30
# Default:
# Timeout=3

# This is a config file for Zabbix internet service daemon agent
# To get more information about Zabbix visit http://www.zabbix.com

### Option: Server
# IP address of Zabbix server
# Connections from other hosts will be denied
# If IPv6 support is enabled then '127.0.0.1', '::127.0.0.1', '::ffff:127.0.0.1' are treated equally.
#
# Mandatory: yes
# Default:
# Server=

Server=192.168.1.197
Hostname=PHPMotion

############ ADVANCED PARAMETERS #################

### Option: Alias
#
# Mandatory: no
# Range:
# Default:

### Option: Timeout
# Spend no more than Timeout seconds on processing
#
# Mandatory: no
# Range: 1-30
# Default:
# Timeout=3

### Option: Include
# You may include individual files or all files in a directory in the configuration file.
#
# Mandatory: no
# Default:
# Include=

# Include=/etc/zabbix/zabbix_agentd.userparams.conf
# Include=/etc/zabbix/zabbix_agentd/

####### USER-DEFINED MONITORED PARAMETERS #######

### Option: UnsafeUserParameters
# Allow all characters to be passed in arguments to user-defined parameters.
# 0 - do not allow
# 1 - allow
#
# Mandatory: no
# Default:
# UnsafeUserParameters=0

### Option: UserParameter
# User-defined parameter to monitor. There can be several user-defined parameters.
# Format: UserParameter=,
# Note that shell command must not return empty string or EOL only.
# Example: UserParameter=system.test,who|wc -l
#UserParameter=system.test,who|wc -l
### Set of parameters for monitoring MySQL server (v3.23.42 and later)
### Change -u and add -p if required
#UserParameter=mysql.ping,mysqladmin -uroot ping|grep alive|wc -l
#UserParameter=mysql.uptime,mysqladmin -uroot status|cut -f2 -d":"|cut -f1 -d"T"
#UserParameter=mysql.threads,mysqladmin -uroot status|cut -f3 -d":"|cut -f1 -d"Q"
#UserParameter=mysql.questions,mysqladmin -uroot status|cut -f4 -d":"|cut -f1 -d"S"
#UserParameter=mysql.slowqueries,mysqladmin -uroot status|cut -f5 -d":"|cut -f1 -d"O"
#UserParameter=mysql.qps,mysqladmin -uroot status|cut -f9 -d":"
#UserParameter=mysql.version,mysql -V
----------------------------- ここまで -----------------------------

＞Zabbixサーバから監視対象(192.168.1.11)にping通りますか？

pingは通ります。

# ping 192.168.1.11
PING 192.168.1.11 (192.168.1.11) 56(84) bytes of data.
64 bytes from 192.168.1.11: icmp_seq=1 ttl=64 time=0.391 ms
64 bytes from 192.168.1.11: icmp_seq=2 ttl=64 time=0.019 ms
64 bytes from 192.168.1.11: icmp_seq=3 ttl=64 time=0.179 ms