Auto-Update errored, entire web log inaccessible

My web log is part of a larger site hosted by ReadyHosting; they offer auto-install, and I’ve been using the web log since September 2015. I hate change for the sake of change, so I’m still using the 2014 theme that I spent some time tweaking.

Just about every time I hit the automatic upgrade button, the site errors–

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HTTP Error 500.0 – Internal Server Error
C:\Program Files (x86)\PHP\v5.6\php-cgi.exe – The FastCGI process exited unexpectedly

Detailed Error Information:
Module FastCgiModule
Notification ExecuteRequestHandler
Handler PHP_via_FastCGI
Error Code 0xc0000005
Requested URL https://www.mjyoung.net:80/weblog/wp-admin/update-core.php
Physical Path \\NAWINFS03\home\users\web\b1039\rh.dahkor\weblog\wp-admin\update-core.php
Logon Method Anonymous
Logon User Anonymous

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I generally go to the host, and they reset to a previous version. I was trying to upgrade to 4.9 tonight, and I got the above error message, and found for a while that the site was locked in maintenance mode, and once it was out of maintenance mode all pages showed as completely blank.

I would like to get the web log software up and running, but perhaps more to the point I would like to be able to upgrade the software when upgrades are released without going through this repeated problem of the upgrade failing and the site crashing.

I have CoreFTP Lite, and can do direct uploads, but I’m not at all certain how to go about installing something this size. Last time I backed up the web log it took hours to download.

I am running Askimet and the forum software. I was running Jetpack, but it started erroring a few months ago so I shut it down.

The page I need help with: [log in to see the link]