I have not specifically seen the problems you are describing, but here are some things you can check that come to mind -
1) Use your phpinfo(); test script and look near the top of the listing to see if and where PHP is looking for the php.ini file. Make sure that this matches where you placed the php.ini as part of the installation, otherwise it is not using any php.ini. Also check further down in the listing to see if the mysql extension is shown.
2) There is a path listed within the php.ini for the extensions .dll folder (which is typically a folder within the PHP folder or where ever you installed PHP.) Make sure that the path for the extensions folder is set correctly.
3) The problems don't seem to be related to mysql, but the default php.ini does not enable the mysql.dll. If mysql does not show up in the phpinfo(); listing, find this line in php.ini - extension=php_mysql.dll and remove any semicolon at the start of the line to uncomment it. Restart the web server and/or reboot the server to cause the change to take effect.
4) There is also a doc_root path in the php.ini that must be set correctly.
You might re-download PHP, your copy might be corrupted or might be missing files. Also, all the files might not have been copied onto the server.