Static noise on all radios in house including transistor unit. Turn off monitor static goes.

someone is using a ham radio near it

Well, it IS the squelch level. Most radios do not have an adjustment for this. Take the bad one back, you've done all the tests you can. Good job.

It sounds like your monitor button is stuck and you are hearing the white noise. Try pressing the monitor button on your other radio and see if the noise is the same. If so, your button is stuck. If not...
Sometimes a lot of static can be an indication of a bad or poorly charged battery. To check for this trade batteries with your known good radio and see if it solves the problem.

Check your batteries. Static can be a sign of a bad or low battery. Swap batteries between the units to see if the problem moves to another radio.
Also, check your antenna and antenna connection.
Best regards.

That means that if too much power is going to the speaker or extraneous signals are being picked up by the wiring, it can come through the speakers as static. Stopping static requires finding and eliminating that extra electricity from transmitting through your speakers.
If you're still hearing distortion, turn down the volume on your amplifier until the distortion goes away. If the volume is too low to be easily heard, the problem may be that your amplifier produces too much power for your speakers to handle or that your amp and speakers have different impedance ratings.

The Bose unit is not the problem, there is interference near by causing the operating frequency to pick up static, check all electrical items in the house including the lights to see if the source can be located, if not it is coming from outside.

Static can be caused by a poorly charged or bad battery. Try cleaning your battery contacts with a pencil eraser, on the battery, radio, and charger. Then recharge the batteries and see if the problem still exists. If so, try a battery from a known good unit and see if it stops the static.

If the battery is not the issue, you could simply have environmental noise. RF (radio frequency wave) in the environment is a common problem in urban areas. If you are using the radios in or around computers and other electronic devices, coil the cords to these devices and make them tidy. RF noise can be emitted through the cord like it is an antenna of sorts. Coiling will reduce this effect.

If your radios have PL capability, aka private line code, interference eliminator, turn it on, or change the setting. This should block out unwanted noise and interference.

Best regards.

take out the speaker in question and test it.
a 9v battery is good enough to 'burp' it.
if it makes a scratchy noise when you put power to it then you have a short in the voice coil.
Burping a speaker is just a short power up. Don't hold power to it.
Tap it on and off like a music note measure.

If the noise goes away when you turn down the volume, it means that it starts before the volume control. And if the volume control has no effect then it is the stage after the control.
Transistors, IC's, bias resistors or ceramic capacitors can cause noise.
If you heat up a transistor by touching it with an soldering iron, it might cause the problem to start up. If it does you have found the culprit. You can also try spraying them with Servisol freezer spray which can be got from Maplin UK or Radio Shack USA. This will cool down any part and help detect the faulty ones.

You can possibly diagnose the problem by trying a different speaker,it does not have to be the same shape as the original but it has to have the same amount of resistance (ohms),radio shack might have one that you can try or one from a broken radio ,if you use one with different value it might not sound as loud but we are trying to see if you hear the static or is gone.You need to unplug the unit from the wall,remove the back cover and locate the speaker,disconect the wires and reconect the one to try then plug the set and turn it on,the antenna will need to be reconected too.Is the most simple test you can do without getting in too deep.Let Us know how it goes by a way of a new question or if you need more information.