Hello. We have a website which had a previous memory limit of 12 MB (12 MB in php.ini, and 16 MB in settings.php) and worked previously.
After moving to a new server it started giving memory limit errors and displaying half-blank screen.
We increaded the limit in both files (php.ini and settings.php) and now it works, but I dont understand how is it possible that now it needs a considerably larger amount of memory (it used to work with 12 MB, now it cont work with less than 20 MB).
12 is too low, if you don't use only drupal as it is. Higher is recommend, than more modules you will install, usually 96MB is enough with image processing...
I assume you did not change the OS in the process. Moving from Windows to Linux or vice versa is quite likely to change resource usage.
And this is a long shot, but perhaps you moved from a 32-bit system to a 64-bit one? This would slightly increase memory usage as addresses (pointers) are twice as large on 64-bit architectures, and code with lots of small objects uses plenty of pointers.
On the whole though, we can't tell you much without seeing what changed about the system.
12 MB is really very low. I would tend to ignore it and go on.
Ideas what could have changed, though:
The old server could have had modules installed that reduced memory usage, e.g. memcache
The new server may have to rely on GD library for image processing, while the old server maybe had ImageMagick (which is an external tool and doesn't count towards the memory limit)