Try turning off Auto-Sync File System on the Host Settings> Other settings.

I too had a problem. Upgraded DNN from 3.9.0 to 3.9.5 and things went well.  Then I installed a 3rd party module which caused a crash. I didn't make a copy of the long install log as to what files were placed into which directories.  I should have.
I ended up going back to the 3.9.0, which was now also crashing.  I tracked it down to a DLL that the 3rd party module installed into the Win/microsoft.net/2.0 whatever directory.  Once the DLL was removed, the site came back, could at least get it to load under the older version, 3.9.0.
I left it sit for 2 days.  After that, I did the 3.9.5 update again.  Went well.  Left it run another 2 days and all was well.
I turned on the Auto-Sync.  I also noticed that the Modules Listing page displayed a bunch of Module updates at the bottom of the page, like they weren't installed already.  I compared versions and I figured that I should re-install all the baseline modules just to make sure that DNN was using the correct code, and that the code had been fully installed.... so I started re-installing Announcements, Forums, etc. and that's when the system stopped responding.  It just DIED.
I went into IIS and stopped & re-started the Application Pools.  I went into Start > Administrative Tools > Services and stopped & restarted IIS Admin Service.  Hey, the website was there again.
It's only been a short while and this Peyton Place story isn't finished yet.  I might end up re-installing Dot Net 2.0... but I checked the Add-Remove list, and there are additional 3.0 and 3.5 listings in there... so now I am totally confused... whether to remove and replace all.
It might be easier just to move the websites to another server with a fresh & un-corrupted IIS and its back-end processes.

BarryZ