First you mentioned PHP 5.5 with Joomla 1.5.26
J1.5 is NOT compatible with PHP 5.4 or higher. So your problems may come from there.
Concerning the upgrade of apache, perhaps that you have statement in the .htaccess that would not be recognized.
To check if the problem comes from there, just rename it temporarly to "disable" it and verify if you still have 403 error.
Another potential reason is the "Mod Security" apache module that would be present in the server and that some security rule reject some call.
For your information, we create in 2014
ajmool2win.com that provide the update for J1.5 and we did a lot of fix for PHP 5.4 but we didn't rechecked it for PHP 5.5.
For your information we had to fix a little more than 11,000 PHP notice, warning, error to make it works.
So if you want to continue working with J1.5, we suggest that you remaain with PHP 5.3 that is the latest one supported by Joomla.
Tou also have to consider that the extension installed in your websites are perhaps also not compatible with PHP 5.4 or higher.
So just upgrade Joomla for PHP 5.4 or 5.5 will not be enough.