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Steps to Determine Market Failure...

Market failure is generally defined as the inability of a free market to provide necessary and demanded goods and services, usually due to difficulties in the pricing model. Everyone benefits from roads, everyone wants street lights, but how do we pay for them? The classic example is a lighthouse -- all sailors and their passengers want to be warned of rocks, but who pays for the service?
Market failure is related to the "problem of the commons," or the tendency of farmers to let their livestock overgraze commonly-owned fields. The proposed solution to the problem of the commons -- a problem of collective non-ownership and a lack of moral hazard -- is almost always the State. This is a truly bizarre non-answer -- if the problem is collective non-ownership and a lack of moral hazard, how can the State, which is the very definition of collective non-ownership and a lack of moral hazard, conceivably solve these problems? Pretending to solve problematic grazing by creating a monstrous agency of social violence with the ability to wage war, print money and run up national debts is like curing a hangnail with a nuclear bomb.
There are a number of conditions that need to be met to quality a problem as a market failure. First of all, the demand needs to be strong enough to potentially divert scarce resources into solving the problem. If only one person has a specific ailment, entrepreneurs will be unlikely to search for a cure, since the demand is so low.
If the demand is strong enough, but the solution is impossible, this cannot be called market failure. We would all love to fly unaided, like Superman, but the laws of physics sadly preclude this. The lack of a magical flying suit cannot be called market failure.
If an activity is banned by the State, this also cannot be called market failure. The market has not failed to serve cocaine users in friendly local shops, this solution is just prohibited.
If an activity would not exist in the absence of the State -- or would be so changed as to be almost unrecognizable -- it cannot be called market failure if voluntarism fails to provide it. There would be no war on drugs in a voluntary society, so it cannot be called "market failure" if free people refuse to lock each other up for personal and peaceful activities. In the same way, it cannot be called "market failure" if a truly free market school does not give teachers a few months off in the summer to help with long-gone farming activities.
Roads were taken over by governments -- they were formerly provided by private companies. The same is true of health care, welfare, education, you name it. It cannot be called "market failure" if an activity formerly provided by the free market was taken over by the State.
So -- to qualify as market failure, the following conditions must be met:
1. There must be sufficient demand to drive resource allocation.
2. The price must be something people are willing and able to pay.
3. The solution must be physically possible.
4. The solution cannot be banned by the State.
5. The solution cannot currently be enforced or protected by the State.
6. The solution can never have been provided by the free market.
7. It has to be an important good or service.