Ubuntu Software Center is just another program and will open up even
if not plugged into the internet - it's when you ask it to install
something that it looks on-line :-) Presumably web browsing / e-mail
is working so the internet connection really is live ? You don't make
it clear if this system is what you are currently using to access the
group.

Try running the command below and see if that fixes things, if you get
an error then the error message will be useful !!

sudo apt-get update