i added #!/usr/bin/perl to the top of your program, ran it on my test server and it worked just fine

in firefox, click tools->web developer->network. paste the address of your page into the address bar and press enter. In the lower part of the screen make sure the all tab is selected and click on the line with status 200. the lower half splits into two panes, the right side should have the tab headers hilighted. look for set-cookie in red, and see what is next to it.

if you see  Set-Cookie: "pass=xxxx; path=/; expires=Tue, 27-Jun-2017 08:19:23 GMT" then the cookie is getting sent, and any reason it is not used by the browser is not the fault of perl but the browser.

If you dont see any "set-cookie" line then i suggest you are not running right file on the server. add this to the bottom of your program print 'hi there'; and copy the file to your cgi directory again. now go to your page with the network section still showing, it should now show "hi there" on the top of the screen. If it does not you are not putting your program in the right place. if it does, click on the stats 200 line again, and look on the right under the headers tab for the set-cookie header.