I might start solving the case with core tex filter files - mimetex.linux should be functional and check that you are using other core files of tex filter as well. There was one bug in the past where php error reporting broke images (in php > 5.2) if old tex filter files were used (fixed about a year ago)
Next I might try to check that all permissions of mimetex.linux and old files in moodledata/filter/tex are correct - you need to be able to create/write image files like moodledata/filter/tex/d71585aa298f736567a6c165a7240009.gif with tex filter and I would check if those files exist at all in folder moodledata/filter/tex
Then I would try to find out what could prevent moving/creating of cached tex image files (some disabled functions of php, Selinux,...) or if files are there what could break images (some injected code in source, that previously mentioned error reporting, some strange rewrite rules could break paths,...) - segmentation fault could have some server side reason, not necessarely in mimetex.linux and so on.