Problems with signing in on Xbox

if you say that you can sign in without internet I believe it's something with your connection or connection settings. try restarting your console under the settings or power cycle it. if that still doesn't work you should contact support at support.xbox.com

can i at least be able to sign in?. and play offline

Unfortunately the Ukraine is not a supported region for xbox live and you will not be able to connect to xbox live from that country.

See this page for the countries that are supported:
http://www.xbox.com/live/countries

I tried an account that doesn't have a credit card linked to it and it didn't work too ....

The Xbox support team is currently working on resolving the "Signing in to Xbox LIVE" issues, you can check the status on the following link:

support.xbox.com/.../xbox-live-status

Is there anywhere else to go for support as we are not getting ANY MS support here? I was referred specifically to this forum from another XBox thread? I have been thru trroubleshoorting and some of the MS suggested reasons why some sign on difficulties
happen but none work. So whereelese does one go for support? KInda annoying to have this neglect of support for a PAID service.