Hi,
I am sorry that you are having trouble installing/using the plugin. It was tested on rough conditions like Linux/Windows with PHP 5.3 and WordPress 3.0 (which are ancient) and no problem found (or they’ve been fixed). Probably it is something “especial” about your WordPress installation.
Anyway just stick a bit around I can fix it (if I found it): what is your PHP version? What about your host OS version (the OS where your WordPress installation runs).
Go to the Support tab (of the plugin) and click the “Check PHP Setup” button. You can copy/paste the system info from there. Does your system meet the minimal requirements? The same screen will show you in red what it looks like not working. Give me that info too.
Regarding the “does not back up the file area” it could mean that (for instance) you have not enabled any “Backup target” where to throw the backup. Did you?
You could go to the “Logs” tab then click the “View” button near the “Full log”. It will download locally the full log of your backup attempt. That log could explain many things.
The HTTP 504 error usually means “Gateway timeout” that the server is down or not working properly. Read this: https://pcsupport.about.com/od/findbyerrormessage/a/504error.htm
You can put all these “debug” info in a text file and drop it on a file sharing service (eg: https://pastebin.com/) then give me here the link to download that file. It could help me to track down the problem.