Hi,
I have almost your configuration and for me works webservice for Prestashop
The version of prestashop that i'am using is 1.6.0.9
Apache Version is: 2.2.29
PHP version 5.3
My advices:
1.try a simple tip:
[email protected]/api
2.try to get information about your host,if they using SSH for authentification, or something like that,or some permissions?
3.try your script on localhost with a xampp or wamp host server
4.move .htacces for a test in this case, to verify if a rule is dening you to get the call to webservice
5.enable error reporting: config/defines.inc.php set PS_MODE_DEV to true,and try to view if is throwing an error here
6.delete your picture from post or blur your key,or change your key after you resolve the problem
Maybe your host have some answers for you, in this case.
I hope that is a new point of view for looking about your problem.