Unfortunately, wet wood will not burn. Even when the fire is roaring, wood is dried by the heat before it starts to burn, although in a hot fire this happens relatively quickly.
The key is to find dry wood to get started, and this is usually foung inside fallen wood even if it appears wet on the outside. Standing deadfall is best because gravity will pull the moisture down and leave the top dry. When it rains, the outer layers of wood gets wet, but the inside stays dry. This means splitting logs. A quality axe is best for medium sized wood, up to, say, 8 inches. For larger wood, a splitting axe is better. Logs smaller than 7-8 inches can be split with your large camp knife, such as Busse BM or Basics 9 or 7, CS Trailmaster or Recon Scout, and MANY others.
As with most things in life, preparation is key. Before you light the match, make sure you have LOTS of tinder, made by shaving thin sliver of dry wood into fuzz sticks, and then lots extra!!! Second, you need dry kindling, strips from 1/16" to 3/8" thick, then you need fuel, which should be thicker, 1/2 to 3 or 4 inches, and dry. Then you must have other, not neccessarily dry, 1"-6" diameter split logs ready for drying beside the lit fire. This method takes at least an hour of prep time in environments where dry wood is readily available, and 2 hours when wood is wet. But, this method has never failed me. If you are very careful, you should be able to accomplish this with one or two matches.
Always practice these methods when starting fires on safe, comfortable trips, and even backyard bonfires, so that when you need to have the skills in an emergency situation, you won't have to rely on ( or wish for!) gas or paper to start your survival fire.
Remember, in the bush, fire is number 1! Nothing, barring injury, will spell disaster quicker than hypothermia!
Every time I step foot away from my home or vehicle in the bush, I ask myself, "what if..."! This means I am always confident in my ability to self rescue, and I can enjoy my outing.
Hope this helps.
Jet