does anybody knows what might be broken and how much does it cost to repair?
Cost of repair will depend on what is found wrong and how long it took to find the fault plus the cost of the component.
It could be anything from a blown fuse to a bad switch or a broken wire or a faulty window regulator.
It MAY just be a damaged wire inside the cover over the wires between the door and the vehicle body. Constant opening and closing will eventually damage the wires.
Thank you so much for the reply. I took it to a shop, and they said they need to re-order the motor and with labor is going to be about $500 
I hope they did a troubleshoot before telling you that. Could be an expensive guess if not.
thank you for reply;
Appeared to be very expensive repair?the mechanic installed an ?aftermarket? window regulator and, when I went back b/c it worked with lots of noise, he took it out, so I had to go back to dealer to fix it ? appeared, that the first mechanic also changed the harness that connects to regulator and threw original harness away ? so the whole work at the dealer was little over $1000 ?
But (long story short) I called VOLVO support and after reviewing all the history of my car and such, and meeting with VOLVO rep (at the dealer where I purchased), VOLVO used ?goodwill? money to reimburse the repair!!! 
Good to see you went after them to couch up the money. Kudos to you.