Here's the "sequence of operation" from the Suburban Furnace Service Manual:
Start
Thermostat Calls for Heat
The wall thermostat controls the operation of the furnace by reacting to room temperature, this allows current to flow through the On/Off switch to the module board. The module board constantly checks for a minimum 9.5 volts. If there is not 9.5 volts, the module board will go into a stand by mode until adequate power is supplied. It will then resume normal operation. Upon a call from the thermostat, the module board thermostat circuit will go active. The sail switch circuit is verified as being open. The blower output is energized.
Blower motor starts.
15 Seconds Purge Cycle
The module board will then verify that the sail switch circuit is closed and motor is up to speed. If this circuit remains open for 30 seconds after the blower motor starts, the module board will go into lock out and shut down the blower motor. The module board checks that the gas valve relay contacts (which are located on the module board) are open before the ignition sequence starts. The board has a pre-purge timing circuit of (approximately 15 seconds). This allows the chamber to purge.
7 Seconds Ignition Cycle and Flame Sense
The module board will energize the gas valve and enable the high voltage spark output to the electrode for 7 seconds of ignition time. The module board will then check for flame sense to verify successful lighting of the main burner flame. Sparking will then be terminated and the gas valve and blower outputs will remain energized. If ignition is successful the module board will monitor the flame sense, sail switch and limit switch circuits, and the thermostat inputs during the heating period. The flame is sensed through the spark wire and electrode. Therefore, it is essential that the electrode is properly positioned in the burner flame.
2 and 3 Ignition and Flame Sense Cycles if Required
3 Try Ignition Board If the flame is not sensed after seven (7) seconds, a second 15 second purge cycle will begin followed by a second Trial-For-Ignition sequence. After three (3) Trial-For-Ignition attempts with no ignition of the main burner, the module board will de-energize the gas valve immediately and blower will run for 3 minutes and then shutdown in lockout. Heating Cycle If during the heating cycle, the limit switch circuit opens and remains open for 5 minutes, the module board will go into lock out and shut down the blower motor. If this occurs, the thermostat will need to be reset for the furnace to operate.
90 Second Shut Down
When the thermostat has reached its set point and the demand for heat ends, the gas valve will be de-energized and the flame will go out. The post purge period of 90 seconds begins. When it times out, the blower motor output is removed, and the blower stops.
The above "sequence" calls for several "safety interlocks" to function properly or the sequence will not move forward.
First, the voltage monitor circuit must sense 9.3VDC. If not above that level, the system goes into "lockout".
Next, the sail switch must be OPEN at the start, before the sequence can begin. Then, during the sequence, when the fan switch closes, the sail switch must also close. If that "two step sequence fails" the system goes into "lockout".
Third, the gas valve control circuit opens the gas valve and starts the ignition sequence for 7 seconds. If a flame is sensed, the system advances. If not, then the next step allows for two additional "ignition attempts". At the end of the third attempt, the system goes into "lockout".
Any of those "lockout sequences" will shut down the furnace and prevent operation.
You should be able to download the Suburban Furnace Service Manual here:
http://bryantrv.com/docs2/docs/subntnew.pdf the sequence of operation is on page 24. The pages that follow are extremely important in troubleshooting that sequence. Any lockout will cause ignition failure, so it could be something as simple as a "sticking sail switch" or as "elusive" as an intermittent capacitor on the control board or even a crack in the printed circuit on the board.