As noted in the installation installation guide, you need to set /cache /compile and /icons to chmod 0777 (read/write/execute for user/group/world)

Hmm, it looks like the host have overly zealous usermode settings (we've seen this one before too. ) that are causing created files to not have the correct permissions to read a file the system just wrote, or prevent the webserver from creating a file in a directory it just made.  Can you post the permissions of the cache/hcl_operators directory?