Turned out to be the High Limit switch. The switch had burnt out, which caused the burner not to fire. Turns out when the limit switch senses the heat box is too hot, it shuts down the gas and forces the blower to continue so it will clear the excess heat. When the switch failed it always told the system that the furnace was over heated, so the burner would not come on and the blower would run constantly to try and clear the excess heat.
To trouble shoot this issue I used an ohm meter to test each sensor, to make sure it was open/closed as it should be. Another way to test would have been to use jumpers to bypass the sensor all together, until the faulty sensor was located.
Your furnace is shutting down on limit. There can be a number of causes for this.
Start by making sure you have a clean filter in the furnace. A dirty or restrictive filter can cause this issue. Alternatively you could also have a dirty or plugged up A/C evaporator coil which is located above your furnace. This can also cause a furnace to cycle off on high limit, however is uncommon unless you have run your furnace without a filter for prolonged periods of time. Also if you have a high efficiency furnace, there is more of a chance to have the secondary heat exchanger plug up rather than the A/C coil.
You can also have a blower motor issue. The motor can be faulty or seizing up causing it to not spin fast enough to move enough air through the furnace. Another cause may be that you have a faulty limit that is opening prematurely.
The major issue that can cause this problem is a heat exchanger issue. If your furnace is cycling off on high limit, and everything checks out, you may have an internal blockage of the heat exchanger. If this is the case either the heat exchanger or the furnace will need to be replaced. A combustion analysis of the furnace is required to prove this is the issue.
If you happen to have a 2 stage high efficiency furnace you could have a bad ventor motor gasket which is allowing air to be drawn in behind the motor. Big cracks in the condensate collector pan can also cause this but is very uncommon. You can also have the a two stage gas valve high fire solenoid stuck open, but this is also very uncommon and can only happen on 2 stage furnaces. Also if you have a bryant, payne, or carrier high efficiency, you could have a cold spot baffle leakage that is allowing air to be drawn in between the primary and secondary heat exchanger however this is also very uncommon.
If you think your blower is not spinning fast enough you may also have a bad blower motor, or if an ecm motor, the control board may be bad. If its a fixed speed motor and your getting power to it but its not spinning fast enough it could possibly be a bad blower motor. If you decide to change out the blower motor, make sure to get the appropriate replacement capacitor to go with it. I actually did have the same issue on an older carrier high efficiency furnace a few weeks back. It ended up being a bad blower motor, however the motor spun freely and had no indications of seizing or hard starting.
Best Answer
Here is the basic ignition sequence for a furnace.
If your exhaust motor is coming on, but the gas is not flowing. The first thing you should look at, is the vacuum switch. This switch is used to tell the furnace that the exhaust blower is on, and that the blower will clear any exhaust gases produced. If the switch does not close, the furnace will not light to prevent toxic gases from being spread through the conditioned space.
Check the tubing attached to the switch, to insure it's clear. Sometimes creepy crawlies like to make homes in things like this, so make sure there are no obstructions.
To check the switch...
Professionals will likely use a different technique, but since it's not the safest practice I will not explain it here.
If the switch tests OK, you'll have to move on to the next part of the system. If the switch does not close, replace it and test the system again.
The next thing to check would be the pilot assembly, control module, and gas valves. However these checks are probably best left to a professional.