OK - then you SHOULD be able to install and input Username/Password to get licence.
If something is interfering with that, the other option is to download the 'site key generator' (or retrieve site key from the 'Licence Status' box - from Help ->About Alibre Design) - then use the Site key to Manually apply for another key via the web site account info page. Copy and paste the new key from the web page into the licence key box.
You might have to experiment a bit with the exact detail - I've never had to use the manual method, the automatic method always worked fine for me.
One last thought - the licence key server changed for v2011, you aren't trying to install an earlier version are you? (that would fail, as updating to v2011 switches you licensing process over to the new server which is only for v2011).
If you still can't get a licence key, then there could be an error in the way you account is set up at Alibre - either Alibre themselves or your reseller should be able to check this for you and disable the key from the previous PC (freeing up one key).