I can connect, and old searches that did not complete will download, and searches complete. However, nothing appears in the search window, and I cannot download. Please help!

What version are you running? Have you upgrade to version 4.6.3? here is the link if this is the case:
Click here to download 4.6.3 version of Bearshare

Also make sure if you have firewalls there are configured right, here is guide to help you learn more:
http://www.bearshare.com/help/firewalls/index.htm

Files that you have selected to Download are retained and hopefully resumed between launches... 'Launches' meaning when you restart BearShare after either closing BearShare or a Shutdown of your machine...

Search results, however, are NOT retained between launches...
(And, you certainly would not want them to be retained as they would be, in most cases, hopelessly out of date !)

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