You're talking about your connection to a host (who you want to download a file from) rather than LW's connection (green bars in the bottom left corner)??
If your LW connection is ok, sounds like you're trying to download fake files.

Search again, vary your search terms, try the All Types search. Stay away from files with lots of sources, go for a file with 10 sources or less, or those with a modem source.

For movies, always check a file before download with Bitzi. A file with heaps of sources but no Bitzi rating is often a fake.
How to use Bitzi

For music, try the tips in this thread
How to find music

And for some general info about these fakes
Info about fake files

If it is a problem with LW's connection, check the sticky below for lots of advice. If you need more help, post back with your details. Post #2 of this sticky shows the info that we need.
Connection problems? Check here first!

It's always a good idea to try the free version (LW basic is free) first to iron out any problems before spending money on Pro