Required special php or server settings

At my request, my hosting company upgraded my version of php to v. 7, which promptly broke access to the admin side. They changed it back to 5.6 but I still can't access the admin side. The hosting company has taken the site offline completely at this point until they figure out what is wrong, but they're asking me to find out if there are any special server settings required for Zencart.

And will it be possible to run Zencart under PHP 7? I need that in order to interface with stamps.com for my shipping.

Which Zen Cart 1.5.5 release are you using, e.g. 1.5.5 vs. 1.5.5a vs. 1.5.5e?
Which sub-release of PHP did your host update your site to, e.g. 7.0, 7.1 or 7.2?

Are there any debug-logs in the site's /logs directory?

When you say "can't access the admin side", specifically what happens? Does the login screen display? Do you receive a whitescreen?

P.S. Yes, Zen Cart 1.5.5 and later will run under PHP 7.0 and later.

Sorry, forgot to mark that I'm using 1.55a.

We know this is a server problem. Nothing is logged in the Zencart debug logs--that's the first place I looked. My host has acknowledged that it's a server issue. The error being displayed in their error log is "AH01271: exec used but not allowed in ... " This appears to be a server side includes problem.

The error that I get when I go to my admin directory is (as best I can remember since I can't duplicate it now) the url to my site, followed by the browser specs followed by [an error occurred while processing this directive].

I don't know which sub-release they changed to, but I can ask. They're running a malware scan on the site now and have taken it down completely until that finishes, and basically told me not to call them back until then. But they did ask whether there are any specific server settings that Zencart needs. They have me on a stupid Wordpress VPS, which I didn't want but was told it was the least expensive of the available options and that their people were capable of dealing with other installed software, not just Wordpress. Every time I have a question now, though, they claim that they're Wordpress specialists and can't comment on anything else. We're going to switch to another company in the spring (my company is merging with another one then and will move to their server). But I have to make this work where it is now.

I just found the FAQ that lists the server requirements for Zencart and can email it to the tech I was talking to, so perhaps that will help. But any added comment that I can pass on to them may be of help as well.