Here is what SiteGround support said:
I am glad to inform you that I was able to find the cause of the problem and now start.php is accessible. There was a directive in the .htaccess file inside the public_html, which was not recognised by Apache. It affected the subdomain, because the .htaccess file works recursively for all subdirectories. To resolve the issue I had to exclude the following from the file:
Code:
<IfModule mod_mime.c>
AddCharset utf-8 .atom \
.bbaw \
.css \
.geojson \
.js \
.json \
.jsonld \
.rdf \
.rss \
.topojson \
.vtt \
.webapp \
.xloc \
.xml
</IfModule>
This did fix the problem. I just uploaded AdminTools 4.2.0 onto a test site, and I noticed that it is generating this code (or maybe I am setting something up incorrectly).
TIA.