Modern disposable nappies contain a number of different synthetic materials, including a variety of plastics and absorbant gels. Some studies have shown that they can contain over 2000 different chemicals. (check out
http://www.realnappycampaign.com/ if you want to learn about using alternatives)
You don't say where you live but if you throw a disposable nappy into a bin in the UK it will end up in either an incinerator or, more likely, a landfill site. There is no 'pulping' of waste before disposal.
Biodegradation is the process by which materials are broken down by living organisims. This process happens much more quickly in material such as animal and plant material (and the contents of the nappy!) than in plastics.
Nappies are soft but this does not stop the plastics in the nappy being broken down - basically the bugs that love chomping on things find it much easier to chomp on natural materials than synthetic ones. In fact most plastics break down through the action of other chemicals and/or sunlight rather than organisms.
Some of the chemicals within the plastics leach out (get washed out) of the materials. These can then enter water courses and cause environmental damage, particularly when the UK disposes of and estimated 3 billion nappies each year.
In answer to what takes the longest to biodegrade, there are many things which will never biodegrade. Basically materials which contain no carbon (ie are inorganic) will never biodegrade although they may be degraded in other ways.