If your client locks up when you try to log in, you are most likely experiencing problems with a proxy. This means you don't have a direct connection to the Internet (many businesses are set up with proxies) and the client does not know how to contact the server. If you were able to successfully connect from your current computer in the past, it is possible that your Internet Service Provider (ISP) has changed its proxy settings recently. You will need to contact your ISP for more information.
If you know that you are not accessing the internet through a proxy, you may be experiencing problems with a firewall. If you have installed a firewall recently, make sure that you have listed the client under the programs that are allowed to access the Internet. You may have to consult your firewall's documentation to learn how to do this. Note that even if you haven't installed a firewall yourself, some operating systems come with a pre-installed firewall.
If you are still unable to connect to LiveJournal through the client, you should check if to see LiveJournal.com is actually down. Try going to
http://www.livejournal.com/ in your web browser, or see
http://status.livejournal.org/. Also, be aware that at peak load times you may receive the "Cannot contact server" error because of the high number of users attempting to contact the servers (
http://www.livejournal.com/support/faqbrowse.bml?faqid=116).
The Visions and Semagic Clients for Windows seem to be the clients that most commonly experience this problem. For more information on editing your proxy settings to allow either of these clients access to the internet, please see this post from the HowTo journal (
http://www.livejournal.com/userinfo.bml?user=howto):
http://www.livejournal.com/users/howto/23617.html.
If you've tried all of the solutions above, and you're still having problems, then file a Support Request under the Clients category from
http://www.livejournal.com/support/.