If anyone could do this, it would be great!
I have looked around, searched through Google, but yet no result that worked...
Anyone can do this.... but we're not just going to show you how to do it.
Have you looked at [man]zip[/man] for PHP? Using Zip you'd just use ZipArchive::open and ZipArchive::addFile to add the files you want to the archive.
To use tar or tar.gz or tar.bz, you'd have to be allowed to use the [man]shell_exec[/man] command in PHP and you'd have to use the tar linux command to create a new tar-ball of your files. I don't know what the exact options and what not would be, but you can google for help with the linux tar command.
To do a mySQL backup, just open phpBB and see how they do theirs. Then adapt it to meet your needs. Essentially all you need to do is [man]mysql_list_tables/man and then use a while loop to iterate over each table. First thing you'd do is see if the first 8 characters are "thelinx_". If not, just [man]continue[/man], otherwise you then need to query the database to DESCRIBE tableName to get the fields. Then you iterate through the fields getting the information for each one.
To get the data, for every iteration through the tables, you'd just run a query to select * from tableName and then create your INSERT INTO statement.
Look at SMF or phpBB's Database backup features for more help and some good examples of how to do it.