Warning: imagejpeg() [function.imagejpeg]: Unable to open \'/home/SITENAME/public_html/files/cache/052f225905c1618003df0c5088aec7a9.jpg\' for writing: Permission denied
Sounds like a permissions problem to me, but we can't tell from this end.
If you can FTP (or CD) into that /home/SITENAME/public_html/files/
and see if 'files' is owned by, and has the same permissions as public_html
Then see what permissions they NEED to have for your hosting setup.