Tri-part events

The most obvious issue us that you are using $user variable in your SQL Query that is not defined anywhere.
You need to follow the basic troubleshooting steps i.e. print your SQL Query instead of executing it. Check the article on troubleshooting custom buttons in PHPRunner manual.

You are right about the $user and $userName. I had changed the userName variable in the code, but forgot to change the post on here. My apologies.
I read through the debugging section that you mentioned and even ran the script through a debugger. I could not find the issue.
I have tried echoing the sql statement and then exit the program, but it doesn't display and it doesn't exit the script. I placed it in the "Server" part as:
echo $sql;

return false;

exit();
But, again, that did not show the sql statement and it didn't exit the script either.
So, I moved to the following to the Server part of the button:
$today = date("Y-m-d"); // This did show the correct date when I ran the debugger

$result["unsubscribe"] = $params["unsubscribe"]; // this actually does work when I use the Before area of the button..

$button->getCurrentRecord(); // this works as well. The debugger gave showed me the correct recruitID as the result
IF($result["unsubscribe"] == "Yes")

{

$data = array();

$keyvalues = array();

$data["unsubscribed"] = "Y";

$data["unsubscribedDate"] = $today;

$data["unsubscribedBy"] = Security::getUserName();

$keyvalues["recruitID"] = $button["recruitID"];

DB::Update("recruit", $data, $keyvalues );

}
Next, I removed the Before and After scripts and placed the following in the Server part:
$today = date("Y-m-d"); // This did show the correct date when I ran the debugger

$button->getCurrentRecord(); // this works as well. The debugger gave showed me the correct recruitID as the result
$data = array();

$keyvalues = array();

$data["unsubscribed"] = "Y";

$data["unsubscribedDate"] = $today;

$data["unsubscribedBy"] = Security::getUserName();

$keyvalues["recruitID"] = $button["recruitID"];

DB::Update("recruit", $data, $keyvalues );
This didn't work either. But, shouldn't this last bit of code work in the Server part of the button withoutthe Before and After javascript parts?

Change the $db_exec to just db_exec. (Without the $ sign)