check script for tcp connection

[Halid Faith]

Hello 

I use FreeBSD6.0. I want to use a script to check two or more case. 
My first cases are as below;
First case My Server will check the remote ip address alive or not as icmp 
Second case My server will connect to other remote ip address as tcp protocol like connected or not.

if my server could not see the remote ip address AND not connect tcp connection, My server will send an email me.

How can I write a simple script about that ?

Thanks