Hi Ken,
Thanks for a very helpful post
To add some extra details, if you try to install a plugin in Moodle 2.x and get a blank screen on moodle/admin/index.php, it's probably a memory or code execution problem. If you remove the new plugin directory and all it's files, i.e. revert the changes that are triggering the error, you can then access your site admin settings:
Site administration > Development > Debugging
Set Debug messages to DEVELOPER: extra Moodle debug messages for developers
Then try to install the plugin again. You should get a PHP stack trace that will tell you something like: Maximum execution time of XX seconds exceeded
If this is the case, then following Ken's advice and upping the max_execution_time in php.ini and restarting your server's services should resolve the issue.
Alternatively, you might get a memory exceeded type message, in which case finding and upping the memory_limit setting in php.ini should cure the problem. I usually put it up to memory_limit = 1024M
I hope this helps!