Hi Michael sorry for the issues you are having. I can help out though.
That is strange the Events Calendar is not uploading and not showing in the Plugins page.
It sounds like something is corrupted with the files. Are you able to either go in with ftp or through the cPanel file manager and delete the Event Calender Directory in your Plugins directory?
typically it would in this directory structure:
\wp-content\plugins\
Let me know if you get that deleted and then it works to reload the Events Calendar.