First, the delete option is not available until you actually deactivate a plugin. Not sure if you have already done that or not. The add new being a missing sub-menu is troubling as it should be there. Do you have the add new option at the top of the plugin page or is that missing as well?
Also, are you logged in as an administrator and have you, or someone else, used some sort of permissions plugin to manually set permissions for different user levels? That could cause you issues if set up incorrectly.
What version of WordPress are you running? Have you upgraded recently? These are the first questions I would try to answer in troubleshooting this issue. Without having actual access to the site, I can only suggest a few things to look at.