Well, I'm not sure what is happening. If Joomla is telling you that the extension is installed then it should be installed. However, in your case, there is no evidence that Joomla installed the extension.
I have not run into this issue before. I have a number of questions about your situation.
Which version of Joomla are you using?
Are you using Joomla's FTP layer (when you have to enter your FTP information to install) or not?
If not, is the plugin/system/ folder on your site writable?
Are there any error messages at all during the installation process?
Have you tried to install any other extensions since you first experienced this issue?