I'm working on a Drupal 7 site and recently triggered a fatal error via installation of incompatible modules. Is it possible to disable a module when site is giving fatal error on each page? Specifically without direct access to files or database?
Without access to the server, files or database?
No, there's nothing you can do.
It's the database you need to update, and if you can't get to that externally or locally to run some SQL, you're out of luck.
You could theoretically alter some code somewhere in core to bypass the issue of the broken module, but of course that would require access to the files, at which point you could've just run the SQL via PHP.