You need to be talking to your host, the connection to the database fails for one of two reasons, usually. The first is you have not provided the right password to connect to the database, or, second, the PHP connection is not being made correctly.
It is easy to use one password as 'root' and then use another as the user. Done it myself - doh! The PHP install may not be the version needed to make Moodle run or it is not configured properly. Run the phpinfo() command and check the version number and then check that the database is mySQL or PostGresQL or MSSQL or Oracle. If the versions do not correspond to Moodle requirements, then it is going tobe very difficult to get a working Moodle.
The other thing I have found that has never worked for me is trying to untar/unzip stuff on a server I have not controlled - not that I have tried it often. This is why I suggest you download it to your local machine first, unzip it there and upload the unzipped to your site via FTP. Install it from there.