Null and wolly, welcome both! to the forum!!
Not only do I believe I have the answer to this ?, but also the cause and solution. A clogged impeller doesn't cause the motor to hum, it would sound normal - except there would be no flow and subsequently, no readable pressure on the gauge. The humming is caused by the shaft being seized up by oxidation (most common cause, however it could be a rock wedged inbetween the impeller and housing, but that's rare) However, the fix could be easy or hard:

Easy, remove lid and basket, put a flathead screwdriver (at least 6") into the back end of the housing (the hole where the basket would cover on the back side) angle it up and try to torque it. If you get some movement, replace the basket, re prime the pump and put the lid on and fire the pump up.

Hard, kill the power to the pump, open the back of the motor (using a small 'regular' screwdriver or a 1/4" nut driver to unscrew the two securing bolts - if the problem is what I think, you'll have to use the 'flat'(regular) screwdriver to pry the cover off, and possibly a hammer to get it off) (the bolts won't come out of the cover, so don't waste your time trying to get them all the way out, but be sure that they aren't still 'threaded in') Using a 7/16 open end wrench try to 'lock on' to the back end of the shaft (it's dead center of the pump, has 2 flat sides hidden behind a white plastic ~triangle that has 2 copper strips ending in white plastic rings forming another triangle) Odds are you won't be able to get the 7/16 wrench on it (there's only 1 clear path to get the wrench in there and the shaft usually isn't positioned to accept it ;( ) - watch out for the capacitor (the black tube that's about the size of a 'D' cell battery, if you touch it's posts, you'll get shocked). However, if you can lock on the shaft, work the wrench up and down a few times, if it moves for you put everything back together and fire up the pump, should work. Be sure to look for water dripping out of the bottom of the pump if you get it going, if you see some look at the next paragraph.

If neither of these work, contact me and I'll walk you through replacing a pump, impeller, or shaft seal, hopefully it won't be necessary for you
Sorry to be so verbose, I'll let it go now, if there are ?s - simply ask (I'm trying to describe stuff I do all the time, so it's hard for me to know how clear I'm making the description)

However,late as it is, I promised the probable cause: if you keep your pump in the same area as your chlorine (esp. pucks) the cl gasses released in a ~small area will oxidize any obliging metal in the immediate area, and all metals oblige