Glad to see you haven't updated to OS 10.3.6 (it has some bugs.)
You mean you select a file/song in the search results, press the Download button but nothing happens? Does any error message come up?

Go to LW's Preferences>Downloads & see how many you have selected for Maximum Dwnlds. Do you have at least one? You should have more than one selected.

What type of modem do you have?

Can you do this test (after LW has been open for at least 20-30 mins: Bug Report instructions & sample image Is your result True/False?