Is a person who suffers from a mood disorder (depression and excessive elation) that compels him to look at forbidden things, or to fall short in obligations such as maintaining kinship ties and seeking knowledge, and to commit forbidden acts such as lashing out at his family, excused in Islamic law? And is he held accountable for his shortcomings?

The basic principle is that you are responsible for your actions unless what afflicts you takes away your will. We advise you to consult a psychiatrist, strive against your lower self, do not succumb to evil thoughts, and adhere to the saying of Abu Darda': "Knowledge is acquired through learning, and forbearance through striving for it. Whoever seeks good will be given it, and whoever guards against evil will be protected from it." Also, frequently remember Allah and supplicate to Him.