My Joomla website loading hangs for 30 seconds - php

Question

I have a persistent problem on one of my Joomla 3.03 websites. The script always delays for about 31 seconds between "afterDispatch" and "beforeRenderModule" before the first module that is in the renderlist.
Other websites on my server run fine
The issue is not module related...unpublishing the first module just shifts the issue to the next module in the list.
The issue seems to be template specific, replacing the template index.php with a standard "Hello world" index.php brings the page up immediately, as does switching to another template.
Deactivating js in chrome devtools does not affect the load time, still slow (I also selectively deleted all the script links that were called in the template index.php to no effect).
I am at a loss as to what is causing the issue. I tried php debugging by inserting a php function
function debug_to_console($data) {
$output = $data;
if (is_array($output))
$output = implode(',', $output);
$date = date('m/d/Y h:i:s a', time());
echo "<script>console.log('Debug Objects: " . $output . $date"' );</script>"; }
at the head of the file and inserting
debug_to_console("Introduced break point:");
at break points, but merely inserting the function without the subsequent break points causes the browser to only display "Break point" and nothing else in the browser window (not the console) immediately. this is making it hard to debug the script.
Any ideas? The website used to run fine. I am loathe to updating PHP because that might affect my other websites which all work fine.
Here is some system info:
PHP Built On Linux inbound-smtp.eu-west-1.amazonaws.com. X.X.XX-XX.XX.amzn1.x86_64 #1 SMP Fri Dec 30 19:11:28 UTC 2016 x86_64
Database Version 5.5.52 Database Collation utf8_general_ci
PHP Version 5.6.28
Web Server Apache/2.4.23 (Amazon) OpenSSL/1.0.1k-fips PHP/5.6.28
WebServer to PHP Interface apache2handler
Joomla! Version Joomla! 3.0.3 Stable [ Ember ] 04-February-2013 14:00 GMT
Joomla! Platform Version Joomla Platform 12.2.0 Stable [ Neil Armstrong ] 21-September-2012 00:00 GMT
User Agent Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/98.0.4758.102 Safari/537.36
(i changed some numbers to Xs in the first line).