Hi,
I am quite sure the problem occurs because using a non-unicode characters in the shopping Cart URL.
Because there is no logical explanation that i can provide you about why it doesn't work with IE9.
Shipping and payment methods are loaded by AJAX load, probably non-unicode URL confuse the loading in IE.
I does work in IE10 though:
Attachment ScreenShot2013-03-07at6.32.04AM.png not found
So try this;
Change URL of the shopping cart URL from:
www.timemaniac.ro/ro/coş.html
to
www.timemaniac.ro/ro/cos.html
If you are using a 3rd party SEF URL component (such as sh404sef, then it would be easy). Otherwise, you might need to change it through Virtuemart Language INI file.
I am sure it will start working when the shopping cart URL has changed.
Regards.
Forum Support.