I think I'll have a go at it...it looks like an interesting poem. You're right, though, it isn't an easy one to find analysis of:
My mouth doth water, and my breast doth swell,
My tongue doth itch, my thoughts in labour be;
Listen then, lordings, with good ear to me,
For of my life I must a riddle tell.
Mouth watering is usually a sign of desire, and when one's "breast doth swell" it is commonly a sign of being prideful. The itchy tongue thing could be a sign of being thirsty, but in context with the earlier line that his mouth is watering I would believe this means he is "itching to say something."
"My thoughts in labor be" could mean that his thoughts are coming difficultly (laboriously) but I think it means that he is about to "give birth" to some of his thoughts; i.e. he is about to start speaking his mind.
The speaker asks some gentlemen to listen to what his about to say and to listen well...he intends to tell a riddle about his life.
Towards Aurora's court a nymph doth dwell,
Rich in all beauties which man's eye can see;
Beauties so far from reach of words, that we
Abase her praise, saying she doth excel;
Aurora, mythologically, is the Roman goddess of dawn. She is the one that makes the sun come up and the sun go down. A nymph is a female spirit that is usually attached to a certain location. In this context, a female spirit "lives" near where Aurora holds court. She is "superhot." Words can describe how beautiful she is. "Abase" means to "bring down or reduce," so the poet is saying that she is so gorgeous that men can't find the words to describe her and are stuck saying that she "excels."
Rich in the treasure of deserved renown;
Rich in the riches of a royal heart;
Rich in those gifts which give the eternal crown;
She is very well known and well thought of, "deserved renown." She is also very majestic in a "royal" way, holding herself regally. In short, she has many "treasures" beyond cash...she is a "larger than life" person with the attitudes of a great woman.
Who though most rich in these, and every part
Which make the patents of true worldly bliss,
Hath no misfortune, but that Rich she is.
All of these wonderful personality gifts make her world a "worldly bliss." She has a good existence. She has no real bad luck, other than the fact that "Rich she is." I find it interesting that the word "rich" is capitalized in mid-sentence. That implies that it is a proper noun, but I can't find any meaning of the word other than to have lots of money.
It seems to imply that being "Rich" in all these gifts is both a blessing and a curse for the nymph. It almost feels like there should be something more to this sonnet...some explanation of why she is both rich and poor for having these gifts, but that doesn't seem to be evident here.
It is also possible I am missing some huge piece of this puzzle...some implication that I don't understand or some piece of the much longer book that explains more about this sonnet. I wasn't able to find #38 in order to compare it with this one and see if the theme continues.
I hope this gives you a little direction to head. Good luck to you!