His mood and situation changes throughout:  he begins by being unhappy with who he is and ends begin thrilled by the love in his life: 

When, in disgrace with Fortune and men's eyes,
I all alone beweep my outcast state,
And trouble deaf heaven with my bootless cries,
And look upon myself, and curse my fate,

 When I am out of luck and I am all alone--an outcast in society, and heaven doesn't hear my prayers, and I feel sorry for myself and my situation,

Wishing me like to one more rich in hope,
Featured like him, like him with friends possessed,
Desiring this man's art and that man's scope,
With what I most enjoy contented least;

I look at others and wish I had more hope like that guy or looked good like that guy, or had lots of friends like that guy, or had talents or intelligence like those other guys. What used to please me in my own life depresses me now.

Yet in these thoughts myself almost despising
Haply I think on thee: and then my state,
Like to the Lark at break of day arising
From sullen earth, sings hymns at Heaven's gate;

BUT, when I'm low in these thoughts and hate myself most, suddenly I think of you.  Then my situation, like the lark singing at sunrise, is floating like hymns to heaven,

For thy sweet love rememb'red such wealth brings
That then I scorn to change my state with Kings.

Because I have remembered that I have your sweet love and the richness it brings to my life makes me unwilling to change places even with Kings.

There is no single plight of the speaker. Rather, he is deeply unhappy with who he is and what he has. These lines:
"Wishing me like to one more rich in hope,
Featured like him, like him with friends possessed,
Desiring this man's art, and that man's scope,"

show the speaker envying the hopes of one man, the features of another, the many friends of a third, the art of a fourth, and the "scope" (reach of mind or abilities) of a fifth. He is unhappy with just about everything about himself…until he remembers love.

Greg