Free hosting often has major problems running WP, so you may want to consider finding better hosting.
That said, yes, could be permissions – this may have some more info for you:
http://codex.wordpress.org/Changing_File_Permissions
But it sounds like you may need to ask the hosting company – see if they will help you.
Do you have FTP access? Create an upload folder under wp-content and make sure it’s writeable.
@turtile Making it writable for all users doesn’t work either. I set the chmod to +777 recursively.
But it sounds like you may need to ask the hosting company – see if they will help you.
Have you asked the hosting?