I'll begin new again, by commenting on your new status post with things I see are wrong or confusing. These go along and in addition to with what ewdudley posted.
My issue is that my boiler is overheating in a short amount of time, or, only running a small (15min) cycle before shutting down due to the internal thermostat in the aquastat. If the stat is working right, it will shut it down per the settings on it. So I don't think it is shutting down due to the internal thermostat in the aquastat.
This short burn time is not allowing for the water systems of the house (or zones) to see any hot water, the only signs of hot water are the surrounding pipes and area (in its days of an operational condition it took around 45 mins to get hot water to the zones.) It doesn't matter how short the burn time is - if the boiler is getting hot, the zones should see hot water. So there's a problem on the circulation side of things. And if it took 45 minutes to get hot water to the zones in 'operational condition', then there was a problem then too, because your zones should see hot water in just a couple of minutes if the boiler is hot and there is a call for heat from the zones.
Adjusting the limits does not change the outcome, even when set low it will still fire and heat up to the 220 degrees and shut down. When it shuts down it will not fire back up until hours later once it has cooled down. At what boiler temp does it fire back up again?
The circulators are working, and are hard wired into the house, Wired how? In order for your system to work right, the zones have to communicate with the boiler to tell it when they need heat. We still don't know how that is done here. The fact you have the thermostats jumpered to give a constant call for heat just adds more confusion because that shouldn't be done. So it is a sign of improper system operation and controlling.
and have been purged to check for water. That still doesn't mean the water is flowing. You could have an airlock or bubble somewhere in your zone which would prevent flow. How much PSI is in your system? Do you have more than one pressure guage? Because they can fail - when mine failed, it failed with the needle stuck on normal PSI reading.
The L1/L2 & B1/B2 terminals on the aquastat were tested and give off the 120 volt read. The thermostat is jumped, Why?
and their are technically two, one for the house call (forced hot water usually off), How does the house heat then if the forced hot water is usually off? How is it turned 'usually off'?
and another for domestic water. I think it is still in call for heat once it shuts off, but I am not positive right now. This is also confusing since if you have the thermostat jumpered, there is always a call for heat.
When I power on the switches, the intermittent ignitor starts in a tripped mode with the red light lit. Does it also do this when you turn on the power when the boiler is cold? But this is another sign of multiple issues - the red light shouldn't come on unless there was a problem with the burner itself. Usually when the cad cell interrupts the burn, or if the points don't ignite the flame, or you lose oil pressure. Do you have steady constant oil pressure & what is it?
At this point there is power to the system but the burner is not burning. If I hit that reset the system will then fire and burn. It will run through the quick cycle How quick? How much time?
until it hits the hot mode which it then cuts the power to all of the components so that everything seems dead, So at this point, is there still 120 at L1/L2 &/or B1/B2? If there is now no power at L1/L2, then there is something else cutting power before it even gets to the aquastat. If there is power at B1/B2, then the burner itself is cutting out. But at that point, your circs should still be running and your boiler should cool off rather quickly.
and the power will not come back until the system has sat for at least a few hours and cooled. You need to find out what all still has power at this point (when it cuts out)..
The following parts have been replaced:
Nozzle
Ignition cover
Intermittent Ignitor
Aquastat (used but tested)
Low water cut off
CAD censor
Nozzle
Oil Filter
Large control box
As far as major components, the only ones not replaced are the circulators and the blower motor, and the main burner box. I do not have any way to tell if the blower motor is working or not. This is my next lead at the moment... If the burner is heating the boiler, then the blower is working. That is what makes most of the noise when the burner starts. It can't burn without the blower running.
There are multiple issues here - you really should get a burner guy in. A decent one should be able to figure out what's wrong in short order. Pretty hard for us to do from here without precise systematic trouble shooting & tracing feedback. And more pictures. And maybe an accurate schematic. Of your whole system.