Deleting the content of the cache folder usually is not a big problem, I actually prefer emptying the cache this way as it it faster than doing it via the interface. Therefore I wonder a bit about your problem now. Did you delete the cache folders or just the content of these folders? If you deleted the folders itself, check whether there are back now. If not, create them. Make sure that the permissions for the cache folders are set to 777 as well.
And before you try anything further, make a backup of the var folder and the database.
Before making a fresh install of eZ 3.9 and trying to get the data in there, I would try making a fresh install of EZ 3.8.6 (first try on another server). Then copy the design, the settings, the var/news_site/storage folder into the new installation and replace the database with yours. Empty the cache of this new installation (contrary to your experience it really should not matter whether you do it on the filesystem or not) and refresh the page. If that works, update this to 3.9, if you want to.
