Have you ever used a siphon before? They can take a little getting used to.
Here's a method I used to get my siphon to work...first of all, make sure the bucket you are siphoning the water into is BELOW your tank, not level with it...place the bucket on the floor, let gravity help you. Place the large end of the siphon completely under water, and then turn it so that the large end of the siphon is pointing UP (make sure the large end of the siphon is completely underwater the whole time)...allow any air bubbles to completely leave and float to the top. Then turn the siphon DOWN and if water does not start moving through, put your lips on the end of the siphon and suck for just a second...this should start the water siphoning through.
If you do this and it does not work, take the siphon out of the water, and hold the entire siphon by the middle of the hose, and dump both ends out at the same time...once the siphon is completely empty of water, try the above again. This method has always worked for me.
I hope that was clear, and didn't leave you ever more confused...I'm not sure what you mean by "start with new water." Do you mean starting with a new tank or changing out 100% of the water in your current one? I would not recommend either of these options. You have to remember that if your fish are still alive, they have grown accustomed to the water in the tank. A massive and rapid water change (even if it is a good change) is stressful for fish. Unless your ammonia and nitrite levels are so high that the fish will die, I would recommend keeping up with your partial water changes to bring the levels down. Remember, the water is not the problem, it is what is in the water creating the problem....