Opening a file does not mean that all output that your program produces goes to the file; additionally, perl will only see the exit code of the system call, and nothing else produced by it.

To get what you are tring to do, change the system line to:

print FILE "Status of $a is: " . system("ping -c 1 192.168.1.$a\n");
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Dr. Michael K. Neylon - mneylon-pm@masemware.com || "You've left the lens cap of your mind on again, Pinky" - The Brain