Can't use dynamic pages: fail due to high memory usage

I’m working on a site which can’t display a dynamic (in wordpress’ sense, i.e. the one holding the main loop) page, unless I raise the memory limit by quite a bit and wait for a long (>5 seconds) loading time, otherwise it just goes blank.

“Static” pages with custom templates work fine, posts and archive show no issues either, it’s just the front dynamic page that doesn’t work. Currently the front page is a custom one set up as static in “Settings -> Reading options”, I was asked to add a classic blog type, so I created a “blog” page and set it as “posts page” in reading options, but it goes blank as stated above. If I remove the “posts page” option, http://site/blog shows fine, but the loop doesn’t work.

I have tried everything that came to my mind, but had no luck so far.

• WordPress is updated to latest version
• I tried disabling and even removing every plugin
• I tried with another template
• I disabled every caching system

More details in this question on wordpress stackexchange.

Really appreciate any help, I’m out of ideas.