What does the fact that the goods in an industry are fungible add to a market power analysis if you already know demand is relatively inelastic?
"Fungibility", when referring to goods, essentially means homogeneity -all units of the good are exactly the same from all aspects that matter to consumers (including "exterior" aspects, like location etc), and so one can substitute for another.
If one knows that in a market essentially only one homogeneous good is traded, then one knows that he must look for market-power sources elsewhere and not in product differentiation (since the latter is non-existent), like for example in barriers to entry, cost structure etc.
If "fungibility" is narrowed down to the inherent characteristics of the good, then geographical location or other such aspects, may become possible sources of product-differentiation, and so of market power.
Fungibility is a property coming from the supply side, so by construction is unrelated to the elasticity of demand (which depends on preferences). Therefore it is a useful piece of information on its own.
I will give it a try, we might not be on the same page about the meanings of the words in your question, so I will use an example.
Say demand for coke is relatively inelastic in a particular economy. There is your big firm, Mapsi, is strong in the market, and there are other off brand competitors, such as Coke-Mart, bangCoke etc. Now, in a world in which all consumers are homogenous, we do not have much room for fun-gibility. This world looks something like people interested in buying 2 liter (half a gallon) bottles.
On the other hand, if we have a realistic consumer base whose demands for soda are relatively inelastic, but who are heterogeneous in how much soda they like, then you have an extra instrument for discriminatory pricing. As your product is fungible in the sense I am hoping to communicate, you can start selling 1 liter bottles, smaller cans etc, each of which gives you some extra ability to satisfy your greed, or as it so happens in worldly possessions, provoke your greed even further.
Silly remarks aside, I hope that my guess might suggest some perspective.
I would agree with the first answer. Fungibility will essentially give market power to the existing players. A new player in a relatively inelastic goods market will have to offer something differentiated to snatch some share from existing players because it cannot take advantage of a low cost. This gives rise to problem as with 'fungibility' you cannot differentiate. One example is commodity products like soaps. It is difficult to differentiate and the inelastic demand leaves with you with lesser options. This gives way to attractive packaging, positioning etc to influence demand. That is why there is aggressive marketing in fast moving consumer goods market.