PHP MySQL Multiple Forms and Multiple Submits on single page

You shouldn't make count a session variable, and you should have a single form - you can have multiple submit buttons to it.

In a form, only things between <form> and </form> are submitted.

Here is an improved refactored version of your code:

<?php

// Database connection settings
$host     = 'localhost';
$username = '';
$password = '';
$db_name  = 'inventory';
$tbl_name = 'computers';

// Connect to server and select database.
mysql_connect($host, $username, $password) or die('cannot connect'); 
mysql_select_db($db_name) or die('cannot select DB');

// Perform updates
if (isset($_POST['Update']))
{
    $value_fields = array('school', 'make', 'model', 'barcode', 'location');

    foreach ((array) $_POST['id'] as $counter => $id)
    {
        $user_values = array();
        foreach($value_fields as $field_name)
        {
            if (isset($_POST[$field_name][$counter]))
            {
                $user_values[] = $field_name . ' = "' . mysql_real_escape_string($_POST[$field_name][$counter]) . '"';
            }
        }
        if (!empty($user_values))
        {
            $sql = 'UPDATE ' . $tbl_name . ' SET ' . implode(', ', $user_values) . ' WHERE id = "' . intval($id) . '"';
            mysql_query($sql);
        }
    }
}

// Build select command
$where = array('TRUE');

$filter_fields = array('school', 'make', 'model', 'barcode', 'location', 'serial', 'date', 'processor', 'ram');

if (empty($_POST['filter']))
{
    $user_filter = array_fill_keys($filter_fields, '');
}
else
{
    $user_filter = (array) $_POST['filter'];

    foreach($filter_fields as $filter_field)
    {
        if (empty($user_filter[$filter_field]))
        {
            $user_filter[$filter_field] = '';
        }
        else
        {
            $term = str_replace(array('=', '_', '%'), array('==', '=_', '=%'), $user_filter[$filter_field]);
            $term = mysql_real_escape_string($term);
            $where[] = $filter_field . ' LIKE "%' . $term . '%" ESCAPE "="';
        }
    }
}

$sql = 'SELECT id, school, make, model, barcode, location FROM ' . $tbl_name . ' WHERE ' . implode(' AND ', $where);
$result = mysql_query($sql);

// Output
function safe_output($str)
{
    return str_replace(array("'", '"'), array("&#39;", "&quot;"), htmlspecialchars($str));
}

?>

<?php include('nav-bar.php'); ?>

<form method="post">
    <h2 align="center">Filter Computers</h2>
    <div style="margin: 0; text-align: center;">
        <p><label>School Name:</label><input type="text" name="filter[school]" size="8" value="<?php echo safe_output($user_filter['school']); ?>" /></p>
        <p><label>Make:</label><input type="text" name="filter[make]" size="25" value="<?php echo safe_output($user_filter['make']); ?>" /></p>
        <p><label>Model:</label><input type="text" name="filter[model]" size="25" value="<?php echo safe_output($user_filter['model']); ?>" /></p>
        <p><label>Barcode:</label><input type="text" name="filter[barcode]" size="12" value="<?php echo safe_output($user_filter['barcode']); ?>" /></p>
        <p><label>Location:</label><input type="text" name="filter[location]" size="25" value="<?php echo safe_output($user_filter['location']); ?>" /></p>
        <p><label>Serial:</label><input type="text" name="filter[serial]" size="25" value="<?php echo safe_output($user_filter['serial']); ?>" /></p>
        <p><label>Date Acquired yyyy-dd-mm:</label><input type="text" name="filter[date]" size="8" value="<?php echo safe_output($user_filter['date']); ?>" /></p>
        <p><label>Processor:</label><input type="text" name="filter[processor]" size="25" value="<?php echo safe_output($user_filter['processor']); ?>" /></p>
        <p><label>RAM:</label><input type="text" name="filter[ram]" size="25" value="<?php echo safe_output($user_filter['ram']); ?>" /></p>
        <p><input align="center" type="submit" value="Filter">
    </div>

    <strong>Update Multiple Computers</strong><br> 
    <table width="500" border="0" cellspacing="1" cellpadding="0">
        <tr>
            <td align="center"><strong>Id</strong></td>
            <td align="center"><strong>School</strong></td>
            <td align="center"><strong>Make</strong></td>
            <td align="center"><strong>Model</strong></td>
            <td align="center"><strong>Barcode</strong></td>
            <td align="center"><strong>Location</strong></td>
        </tr>
<?php while ($row = mysql_fetch_array($result)): ?>
        <tr>
            <td align="center"><input name="id[]" type="hidden" value="<?php echo $row['id']; ?>" /><?php echo $row['id']; ?></td>
            <td align="center"><input name="school[]" type="text" value="<?php echo safe_output($row['school']); ?>" /></td>
            <td align="center"><input name="make[]" type="text" value="<?php echo safe_output($row['make']); ?>" /></td>
            <td align="center"><input name="model[]" type="text" value="<?php echo safe_output($row['model']); ?>" /></td>
            <td align="center"><input name="barcode[]" type="text" value="<?php echo safe_output($row['barcode']); ?>" /></td>
            <td align="center"><input name="location[]" type="text" value="<?php echo safe_output($row['location']); ?>" /></td>
        </tr>
<?php endwhile; ?>
        <tr>
            <td colspan="6" align="center"><input type="submit" name="Update" value="Update" /></td>
        </tr>
    </table>
</form>

There is a lot to learn here:

1. Separate the output or view (HTML) from the logic and processing code, the most possible. Note that the HTML starts only at the end. We have the least possible PHP code mixed with the HTML.

2. If you don't clean your input ($_POST) and output (echo) you are vulnerable to several types of attack, like SQL injection and XSS. So, you always need to clean the user input before using it and the output before echoing it.

3. To build both the UPDATE and the SELECT queries, we are using the implode function together with an array ($user_values for the UDPATE and $where for the SELECT).

4. We are making the UPDATEs before the SELECT so the output appears updated.

5. The LIKE clause is complicated to build correctly, because the user may want to search for "100%", but this percentage character can't be confused with the percentage of the SQL command. This is why we have some complicated and mysterious lines of code in this part.

6. The mysql_real_escape_string and intval functions take care of cleaning the user input.

7. We have made a safe_output function using htmlspecialchars and str_replace to clean the output.

8. We have made an effort to have a complete $user_filter array arriving at the output phase.

9. When the HTML starts, we have done everything: the safe UPDATES, the safe SELECT, the filters are in $user_filter array, and the results are in the $result resource. We only need to output.

10. In the HTML, you can't have multiple elements with the same ID, and you don't need an ID for every form input. So, I removed the useless IDs.

11. I have renamed the filter input names. Take a look. This way, we can have an array of filters.

12. In this case, the "tabindex" attributes were useless, so they were also removed.

This is what hidden inputs are for. Add one for your id:

<input type="hidden" name="id[]" value="<?=$rows['id']?>" />

Also, you don't need to save the count. You can count the number of items in an array using count($id).

Finally, sanitize your inputs. Never put user submitted data straight into a query. Use intval for integers and mysql_real_escape_string for strings, or use prepared statements.