Ok. I watched your video. Mechanically, your flute does not appear to have any serious problems. All the keys seem to close and return as they should. I'm not certain if Bb key is opening properly. In some shots, it appears to be too close to the tone hole but you may have pressed the thumb Bb key. If not, that may indicate an unhooked or broken spring. Some keys normally stay closed, but I could not see those well enough to tell if there were problems with those. I hear some clicking when you move some of the keys and that is likely caused by missing corks or felts under the kicker (foot) of some keys. That will not keep the flute from playing. Clicking could also be a missing cork or felt that is used to adjust the key regulation and that could cause some notes to not play.
The dent in the headjoint may cause some very slight intonation problems but that would not keep the flute from playing either.
One thing that I did see (at 01:19 seconds in the video and at 03:39) is that the screw for the thumb B key appears to be unscrewed slightly. If the screw is out far enough, it could cause the B key not to seat properly and leak. If so, that would cause problems with any note B or lower. If you have a jeweler's screwdriver set, find one that closely fits the screw slot. It should not be too large or too small. Gently screw it in (clockwise) until you begin to feel it get snug. Don't over tighten it, just tighten until you feel resistance. I took a second look at the video and I also noticed (at 00:09 and 02:14 seconds) that the screw on the G keys is not screwed in. That could cause the G keys to leak. Tighten both those screws and see if that helps it play better. Also, it looks like (at 02:50) the second (lower) G key is not completely closing when the E key is pressed. Your flute has a "Split-E" feature, but it doesn't look like it is adjusted properly.
From the video, it's difficult to tell if any pads need to be replaced. In the video, you sometimes moved the camera too quickly to really get a good look at where the pads seat (cover) on the toneholes. The pads appear to be a bit dark in color, but that could be a shadow - stronger lighting on the pads would make it easier to see them. If they really are quite dark, they may just be old and might need to be replaced. Even if the pads look OK, they may or may not be seating properly. You can assess whether each pad is seating AND sealing properly. To do that, you will need a small strip of thin paper. Cut a few strips about 1/8 inch wide and about 2 inches long. Glue or tape one end to a wooden match stick or other similar piece of wood or plastic. To test each pad, stick the end of the paper under a pad and into the tone hole below. Gently close the key onto the paper and while holding it gently closed, pull the stick slowly to pull the paper partly out. If the paper tears, you are putting too much pressure on the key. If you feel resistance, the pad is seating at that spot. Move the paper around the tone hole and test the resistance at about 6-8 places around the tone hole. In other words, looking at the top of the key, test at the 12 O'clock position, then 2 O'clock, 4, 6, 8, and 10 position. If the resistance feels the same at each position, the pad should be seating OK. If you find that there is much less or no resistance when you pull the stick, that means the pad is leaking. You'll have to do this procedure on every pad. This is tedious, but that is one method that a repair tech can use to assess the condition of each pad. Also look for any tears or holes in the skin covering of each pad. If you find any tears or holes, you have found a leak.
Use these inspection sheets to help guide you to annotate any issues. Let us know what you find...
http://www.musictrader.com/flutevisualinspection.pdf
http://www.musictrader.com/fluteinspectionsheet.pdf
. I asked in a shop for the repair costs and they told me 80euros... 
