Peerless Boiler - Turned off boiler to replace Circulator for the hot water. Turned furnace back on. Did not ignite. Tried to hit the reset button for 30 seconds and nothing happened. Furnace will

It sounds like it has been mis-wired. The circulator pump should run all the time the boiler is on and should continue to run when heat is called for so it circulates the water in the radiators as it cools. There is normally an electronic valve that shuts flow to the radiators when only hot water is needed. Call for heat and that valve opens. It sounds like you need a mature, old school boiler / central heating technician who has lots of real world experience with older boilers.
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If you have a large screwdriver, you can use it against the pump as a stethoscope to listen for the pump running. The noise is very distinctive.

Is the control that operates the pump located in the storage tank? If so the pump not be pumping. A few factors might be needed to solve the issue.

Do you have power to the boiler? Is it gas or Oil sounds like oil. If so when was the last tune up? Need more info .

Draining is the easy part. Isolate the water feeder (shut off). Open hose bib @ boiler, & open the expansion tank valve to pull air in to allow more water out.
Refilling- let the water feeder fill -should be around 12 Psi, then go around the building to all the baseboards or radiators & open the bleeder key valves to let the air out until you get a steady stream of water. Most of the air should work its way to the expansion tank. Turn the boiler on & test your new pump.

Dean,
What kind of primary control? Beckett?Honeywell? Carlin? Control model #?

Check out this site
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There should be a control called an aquastat that regulates the temperature of the boiler. The thermostat will turn on the circulator to start the flow of water through the radiators. If the water coming back from the radiators is very cold, a control will shut off the circulator until the boiler can come up to a predetermined temperature then start the flow of water again. If you have a tankless coil for domestic hot water, you now have a triple aquastat that maintains the temperature for domestic as well as the boiler temp. So yes the boiler thermostat (aquastat) does control the heat of the radiators and domestic hot water. No the pump is regulated by your house thermostat. You should take an amp draw on the boiler and componants to find out what is drawing more electricity than it should and popping your fuse.

From what you are saying it sounds like an issue with either a circulator pump or a zone valve. It depends on what type of system you have ... if you have a circulator pump that only runs the Amtrol then that is probably bad. If you have a zone valve system then it is probably the zone valve if you still have heat for the rest of the house. If you have no space heating then it is probably the circulator pump.

Check all your limit switches on this unit. One of them is either tripped or bad.