Sounds to me like she needs a play partner.  She's got all this kitten
energy that needs to be let out in practice fighting, and you're the only
one around to let it out on.  Can you adopt a buddy for her?  She really
needs another cat to learn with about acceptable levels of violence, what
hurts (her and the other), and so on.

BTW, my Benjamin didn't like being picked up or cuddled as a kitten.  I
had to firmly hold him on a surface and pet him to teach him about
petting.  Before he was full grown, it was like I hooked him on heroin.  
He couldn't get enough.  Didn't want me to pick him up, though, and wasn't
a lap cat.  Now, five years later, he's become a lap fungus.  He still
doesn't want to be picked up, but if I sit in the recliner in front of the
TV, he'll come drape himself across my lap and purr.  (He's also the one
who from early adulthood on assigned himself as my bed monitor.  He
oversees my teethbrushing, etc., makes sure I'm settled in bed, collects
some pets, brings me a toy (usually), then goes off on his own business.  
In the morning he'll lick my arms or lie on top of me to wake me up.)

Priscilla

4 weeks is very young. She didn't get the interaction she needed to
teach her that biting hurts - interaction usually supplied by Mama and
siblings between 3-8 weeks of age. If you can't get another kitten or
cat for her, you'll need to teach her how to interact.
She is probably interpreting your petting as an invitation to play,
especially if you pet her along the top of her head, neck, or her rump.
All of these are areas other cats will grab to invite play. Petting
along the stomach often induces fear aggression in cats, especially
females. This is just instinct.

Be very, very patient - this can take a while.

Every time she bites you too hard, give a high-piched "Ow!". If she
doesn't immediately stop, put her down away from you and ignore her
completely (don't even look at her) for at least 5 minutes. If she
continues to follow you to bite (many cats do this in play), confine her
to another room for 5 minutes. You might find yourself having to do this
constantly for a couple days. Each time she plays nice and doesn't bite,
praise her. Offer a treat if she likes them. Keep play and petting
sessions short so she has a chance to succeed at not biting. Lengthen as
she progresses. In the meantime, don't invite her to fail - if you know
she bites when you pet her, don't pet her unless you're doing a training
session. Play with toys instead for interaction.
Do training sessions often, but keep them very short. The more chances
she has to succeed at not biting, the faster she'll learn it is better
and more fun for her that way.

Try to see if her body language allows you to catch her just before she
bites (flattened ears, a twitch of the tail, a stiffening of the body).
If you can, catch her just before she bites and set her down away from
you, but don't ignore her. Just talk nice to her and play with a toy
(not your hands) that she can bite, such as a stuffed animal. Redirect
her desire to bite you onto the desire to play with her stuffed toy.

Another kitten or cat would be ideal, as they provide a nice outlet for
rough play as well as a nice teacher for bite inhibition and
socialization.

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~kaeli~
Hey, if you got it flaunt it! If you don't, stare
at someone who does. Just don't lick the TV screen,
it leaves streaks.
http://www.ipwebdesign.net/wildAtHeart
http://www.ipwebdesign.net/kaelisSpace
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