If you have Internet Explorer, look for a little "gear" like icon in the upper-right corner of the screen.
Click on the gear icon, then select "Internet Options" from the menu (near the bottom of the list). In that Internet Options menu, you will see several tabs at the top.
Click on the one marked "Privacy." On that screen, near the bottom is a check mark for "Pop-up Blocker." Un-check that box and click the "Apply" button at the bottom. Then, try to get your messages again. If they work now, they you can use the "Settings" button next to the Pop-up Blocker line to add "www.ancestry.com
" to the list of sites that will not be blocked, and Check the Pop-up Blocker again to turn it on (to prevent annoying pop-ups).
I'm using Internet Explorer 9 in Windows 7, so other versions might be slightly different, though all of them will have most of the same options somewhere.
If this is too technical for you, then I would suggest calling Ancestry support and let them walk you through their processes on the telephone.