Not sure what 'shared cluster' actually means in RackSpace terms, but sounds like you have a Linux flavored setup (total guess really) and that you have ssh access and can su to root user. IF it is linux, try installation via command line. the CLI install doesn't use apache nor your browser (where this issue in installing might lie) and uses less memory on server.
Assuming your server setup meets the requirements for 2.6 - min: PHP 5.3.3, MySQL 5.1.33
Is MySQL service on the same server where you are installing the code/data directory?
Drop your current moodle 2 db - it's incomplete anyway.
After you have setup another moodle db (character set utf8 collate utf8_general_ci) and have created a moodledata directory (readable/writeable by apache user), and have uploaded (acquired the 2.6.1 code) and placed it in document root of the server, then ... as root user:
cd pathto/moodlecodefolderatdocumentroot/admin/cli/
php install.php [ENTER]
The install screens are text based and will prompt for the same items asked via the web based install.
'spirit of sharing', Ken