Depending on how many incomplete & shared files you have, LW takes some time to load them all up & try to connect to each individual incomplete file one by one. It's best to leave LW alone for some time (perhaps 10-20 mins before doing anything with it.) LW is primarily a downlding program so that's where its 1st priorities always lie. If its resources are too busy searching & downlding &/ loading, etc., then all its resources will be used up & LW's media player may suffer. If you still suffer issues after 30 mins with lw then it's probably best to disable LW's media player so that your default player will open & play all launched songs instead. (Tools>Options>Player & untick option & press Apply.)
If you don't have a decent mp3 player try QCD (it's free & has built-in codecs & plays everything):
http://www.quinnware.com/
I forgot to mention, the files in your LW LIbrary window will not be available to play until LW has properly loaded them & accounted for them all. As soon as you open lW & go to LW's Library window you will notice these shared files are all RED. But one by one they will turn black. Not until they have turned black can you launch them.