Let's split the problems into two categories, proximate and fundamental. It is easy to confuse the two categories or mix the problems of fundamental nature with those of proximate. Econoimc historians, in the pursuit of determining the causes of Britain's industrialisation have come up with several plausible explanations. I think we can use their framework to explain why Pakistan faces economic problems. I believe these factors are relevant in this case - Pakistan has not been able to take off from the low growth state for a while now. If I remember, it was a success story in the 1990s, but it could not sustain its high growth. In that sense, the country faces Malthusian straightjack.
Quality of Institutions. Every since North and Weingast (1989) claimed that Britain's take off in the eighteenth century was possile thanks to its Glorios Revolution when the Crown transferred much of its power to the Parliament. With this transformation, Britain was able to lift itsel from centuries of low growth state, first in the world. Does this give any explanation to why Pakistan faces the problems it has had for years. I would say it does. First. The quality of institutions is poor in Pakistan - rules of the game are not enforced properly. The political and social setting is not condcuive to growth - property rights are not secure, corruption is rampant, it is, possibly, institutionalised, and the presence of the rent seeking political elite obstructs the enforcement of rules. The necessary institutions have eveloved there, but they do not function in a way that permits growth. Daron Acemoglu (MIT) has successfully built on North's work, Acemoglu has a nice book on why nations fail. I would recommend you to read it.
Culture. Joel Mokyr has been putting the idea of 'cultural supremacy' in centrestage to explain the Industrial Revoltuion. I think his ideas could as well provide some explanation why Pakistan is facing problems. Historically, Mokyr believes, the beliefs, values, and preferences in society that are capable of changing behavior were a deciding factor in societal transformations. He goes on explaning what these transformations were and how they lead to the take off of Britain. Does Pakistan have the type of culture Mokyr is referring to, possible yes, but it is suppressed due to the presence of the issues outlined above in point 1. (will continue later)
Ideology/Religion. Pakistan is a hotspot of religious conflicts. The conflicts are not between religions but within religions. Tribes fighting tribes and depriving the young generation from education (girls and women especially). Such a culture suppresses innovation and discourages innovative behaviour. There is a growing literature on the role of religion in economic growth. Consensus has not been achieved as in other areas, but the papers look into catholicism vs. protestant vs. anglican vs. bhuddism vs. islam vs. judaism etc. vs. growth. It is probably not possible to quanitify religion's role in growth precisely. There is a misconception that religion suppresses innovation. Some papers point at the events of the past, there have been many including the locking up of Galileo for his claims about solar system which we today know were true. Pakistan is an Islamic country (in fact, it is Islamic Replublic of Pakistan). Does Islam hinder growth there? The facts point at No. Islam, like any other religions, promotes peace, grwoth and wellbeing but people adhering to Islam do not follow the teachings correctly. Economic historians agree that during the time of Abbasid Caliphate, Muslims had their golden age. It would not be an exaggeration if I claim that muslims were the only people making progress in all aspects of life at the time. Much of the World was in turmoil (Europeans had not seen a long lasting peace until nineteenth century, spurts of wars hindered growth for a long time). Exceptions could be given to the nations of the Far East (China). So, what is the issue here, it is surely the individuals and groups wages conflicts between various religios factions. These acts do not promote growth.
The other factors (i.e. low investment, human capital, terrorism, etc.) causing the problems are generally proximate.
(I will add more as soon as I have time)