I'd say the door is open on this one.
Worn parts typically do not create a shake. They do nothing to control it thus it can easily make things worse than they are (worn shocks/struts ect).
Has the car been wrecked, or curbed real bad?
Here are some thoughts:
Bad tires; tires DO slip belts, they do go out of round and IF someone skidded the car on dry pavement (perhaps w/out your knowledge) a good set of new tires can shake.
More likely is you have bent wheel or a bad tire. Less likely is a bent hub or a stiff axle joint.
Options:
A) take it to a shop and have them spin all four tires and check for wheel run-out, wobble, eccentric tire movement (out of round).
B) redo the balance. Rookies can get it done fast, but can make mistakes.
C) Leave the wheels on, support the car on a rack on the control arms all wheels in the air. Place car in low, and let it idle. Watch the fronts for trueness. Spin the back by hand and check for the same.
D) have someone follow suspect car while both doing 5 - 7 mph or less and see if the body of the car sways from side to side (a slipped belt in the tire only seen under load at low speeds.
E) If all of that leads to nothing, Spin balance the tires ON THE CAR! Only a handful of shops will have this ability. It uses a sensor under the axle being balanced, and powerful motor to spin the tire from a rotor like device touching the sidewall. A strobelight tells the tech where to place the balance weight. This process often resolves balance issues when others fail. On car wheel/tire balancing.
http://www.hunter.com/PUB/PRODUCT/ba...0T-1/index.htm
PS - most drive line related vibes occur at speeds after 44mph.