[Typo3] Problem with Domain redirection to typo3

[rafaelm at poczta.onet.pl]

Hello,

I have a really strange Problem.
I had correct working typo3 and it was called by domain e.g. www.blabla.com.
I copied files to other server (new one) and updated (from 3.6.2 to 3.8.0). When I call directly e.g. newserver.com/~myaccount/typo3/site/ then I see  correctly working site. BUT when I call by this domain (my domain is assigned with this link) then I wait long time and comes error message from the browser - that site cannot be displayed.
So the site works but only when I call directly, not by the domain (which is assigned by external service).
I started to analyse source code of typo3 and I saw that it "crashes" in /index.php on the line:
echo $GLOBALS['TSFE']->content;

The new server is more secured. Firewall blocks almost all ports. When we turn off the firewall, then it works !!
It seems that typo3 + redirection requires "something".
Does anybody know what do I have to configure ? What can I do with that ?

I'd very greateful for help.

with best regards,
Rafal