Re: Class Problem/mysql :(
From a quick examination of the code you have posted (please use [php][/php] tags next time), you appear to have omitted the processing instruction name from one of your code blocks in "Engine Core.php".
While there is an option to have PHP interpret <? ?> as code, it is not a default option and is considered bad practice as it may conflict with other processing instructions (e.g: <?xml). The debugger may be configured with this option enabled (you can check this with a call to phpinfo()) and search for short_open_tag.
To get rid of your nasty error, ensure that all PHP code is enclosed within <?php ?> and not <? ?>.