If you can put up with people on here at times (including me), you can deal with a knock-back or two, I'm sure. Also, you'd be surprised how many times those people who say 'no' now, will come back to you in the future and ask you to do work for them. Happened to me on plenty of occasions.
I've found a few jobs through LinkedIn, but not a huge amount (I think there's an 'open to work' or 'looking for work' tag you can put on your profile.
When I went freelance, I approached pretty much all of the contacts I had for work. Some titles I still work for now, but others have come and...