The speaker tells us that his hair has all gone gray, but not because he's old.
And it didn't all turn white suddenly because of a traumatic event.
The speaker says that his legs are "bow'd," or bent, but not because of hard labor – it's more like his arms and legs have "rusted" with lack of use.
And he hasn't enjoyed the lack of use – it's not like he's kicking back and enjoying being lazy. He calls it "vile repose," or evil rest.
His "limbs" have been "spoil[ed]" by a dungeon. This is the first mention of the setting of the poem (besides the title, of course).
The speaker says that he has shared the same "fate" as people who are "bann'd and barr'd" from fresh air and freedom.
The speaker tells us that his imprisonment is the result of his "father's faith," but he doesn't give any details on what, exactly, his "father's faith" was.
It could be his father's political beliefs or his father's religious faith – either way, the speaker says that he was thrown in prison along with his brothers (the whole "lineal race") because his father wouldn't give up his beliefs.
He also says that his father died by being burned "at the stake" for his beliefs.
The speaker says that there had been seven people in his family (their father, and his six sons), but now he's the only one left.
The six that died all died as they lived – proud to be "persecut[ed]" for their beliefs.
The speaker starts listing how all his brothers died.
One of them died "in fire," so probably by being burned at the stake, like their father (line 13). Two of them died on the "field" of battle. Those first three all died like their dad – for believing in a "God" that their enemies "denied."
So here it seems like the family is being persecuted for their religious beliefs, but elsewhere in the poem it's more ambiguous.
The other three were thrown into prison, and the speaker is the last of the three to survive.
He calls himself a "wreck" because he's so old and "grey" (line 1) from his time in prison.