Brand new. Pulse feature stuck ON. Tried OFF. Tried unplugging. Still only pulses, no blending. Tried a dozen times.

Is probably a binding problem with the motor shaft bearing or the circuit card is fried. If you've tried giving it a good cleaning and that didn't work it's a good bet the unit is junk. Suggest buy a new one.

try pulse mode

It Could Be a Number of Things..
It's most likely that the electrical Wire Could Have a Shortage, If it cuts off again Try gently Wiggling the Electrical Wire in a Number of Directions If it cuts on and off while your fidgeting with it, you've found your Problem! A quick fix would be to Adjust the wire In the position it would cut on the strongest, wrap the cord with Tape to Keep the wire in that Position, this will Prevent it from shorting again.
Either that or you simply put too much product in the Blender with an inadequate amount of liquid.

Probably going to require a new 3 button switch panel, they are not hard to fit.

The motors even if they not old blenders if they have work with too much load for along time then they have been overheated and thus they will trip overheat safety more sensitive. So now actualy you have less blending torque as you have describe. So now their is much posibilty if you continue to work it the same way you will finally burn the motor rotor so the damage will be grait.
So now not only you can not get more torque but you should try to avoid very heavy use in order to have them work for a longer time.
When you use with a lot of ice cubes try to cover them with a lot of liquids and always use the pulse mode to start ant the continues rotation.
Good luck

This worked for me - only took about 5 minutes (the amount of time it took for me to google Black & Decker and search through their FAQ)

Q. My blender stopped in the middle of blending. What happened?
A. Your blender has a motor overheat protection system that will automatically shut off the blender when it has been running too long with a heavy load. If this happens, unplug the blender and wait 10-15 minutes to allow the motor to cool down. Plug in the blender and resume blending.

Frozen elements are generally not recommended for blenders of any brand. They may cause the blade assembly to stop moving completely, or to "bog down," and this may eventually damage the motor. It is recommended that frozen fruits and/or yogurt be thawed when possible before placing into a blender. If this is not a possibility for you, I would use a "pulse" or "chop ice" function to rapidly spin the blades for just a moment. This will chop the contents in smaller, more manageable parts. This should be done before adding other liquid ingredients.

You can get this with google.

Otherwise ask manualfox.com - this is the hazzle-less way to get it.

this may sound weird but I had it work on some buttons such as you have on the blender. Get a pencil and using the eraser end tap firmly on the stuck button hopefully it'll release it.
best to you.