hmmm... not sure why they do not provide logs - are there any in your hosting CP?

Without at least a link it is hard to diagnose - but can you ping the site ok from a dos window (start -> run ->cmd -> ping yourdomain.tld) or run a traceroute to it (start -> run -> cmd -> tracert yourdomain.tld)

If these both work fine, then the site is responding.

Do you have logs set up within threads?
Can you FTP in to the site?