Is there any alternative to soldering?

Let me start from beginning. My screen cracked on my BLU studio 6.0. I took advice from previous answers and purchased lcd screen frame assembly. I had the phone apart, waiting for the replacement. Now it seems someone, I say someone because no one seems to knows who did it. The two tiny wires connected to my mic are disconnected. I just spent $82 on the replacement part. Is there any hope for something else besides the soldering. That's one thing I have never attempted before. If need be, where can I find the stuff to do it? Thanks for any suggestions