Hi Peter,
We will try our best to help you out with this issue. Firstly, can you consult with you web hosting regarding to permission to write the following folders (See screenshot:
http://screencast.com/t/n2jmPRKRUX4). As well, can you please advise that, I am also hitting this error while trying to install the latest EasyBlog:
Warning: file_put_contents(): Only 0 of 13 bytes written, possibly out of free disk space
. It seems like, you have limited free disk space. Can you consult this with your web hosting provider?