Thanks Vincente, the eval function is exactly what I needed.
For those of you who want to pull HTML and PHP code from a database field, it is important to note the following:
When you use mysql_fetch_row (or any other fetch method), you'll need to strip the slashes if you have those automatically inserted into your table data, and you also will need to prepend a PHP close tag before reading in the field data. The following (updated) code solved my original problem:
<?
.....yadda connection strings, etc.
//Simple query returns data from one field successfully
$precode_query = "SELECT element_precode FROM elements WHERE pages_id = '$pos' AND subpages_id = '$spos'";
$precode_query_result = mysql_query($precode_query);
$table = mysql_fetch_row($precode_query_result);
eval(stripslashes('?>'.$table[0]));
?>
All this works great for functions, but NOT for variables, by the way! If you want to have PHP evaluate a variable within a database field, you need to make sure your headers have the values declared before the table is queried. Otherwise, when you eval() a field containing a PHP variable, your output will be null!
To get around this, simply use the ob_start() and ob_end_flush() function (and be sure that your ISP or your php.ini has output buffering set to "On"):
ob_start();
$variable = "Anything you want to declare";
$variable2 = "And so on...";
ob_end_flush();
Now everything between ob_start and ob_end_flush is sent to the header before the PHP page renders. When you display the database field that references $variable2, your output will now display "And so on..."
Here's what my database field looks like using a function:
<? echo "<table width=100%><tr><td>Time:".time()."</td></tr></table>"; ?>
That's how the field should appear. You can also do the same for variables:
<? echo "<table width=100%><tr><td>Time:$time_to_var</td></tr></table>"; ?>
I'm embarrased to say how much time this took to figure out. Let me know if this is useful to you!