It is not a external plugins issue. It is a moodle installation problem.
The errors are very clear:
Warning: require_once(/mod/chat/lib.php): failed to open stream: No such file or directory in /home/*****************/moodle/mod/chat/locallib.php on line 23
Fatal error: require_once(): Failed opening required '/mod/chat/lib.php' (include_path='/home/*******************/moodle/lib/pear:.:/opt/alt/php56/usr/share/pear:/opt/alt/php56/usr/share/php') in /home/********************/moodle/mod/chat/locallib.php on line 23
Announcements (forum)
Notice: Undefined variable: CFG in /home/********************/moodle/mod/forum/locallib.php on line 22
Notice: Trying to get property of non-object in /home/***************/moodle/mod/forum/locallib.php on line 22
Warning: require_once(/mod/forum/lib.php): failed to open stream: No such file or directory in /home/*******************/moodle/mod/forum/locallib.php on line 22
Or the files are located in the right folder or moodle can open the files because do not have enough permissions. Those files are part of moodle core and not related with any plugin installed.
If the site was upgraded then probably is a wrong upgrade. Start the upgrade from the beginning and installing new moodle files from scratch.