I have a Tempstar furnace. It is a natural gas furnace and the gas valve and the electrical parts are Honeywell (Gas Valve VR8204M1075, Control Module ST9120C4057, Ignition Module S8600M1005). The furnace is about 10 years old. When I tried to turn it on for the first time this year it would ignite for a bit and then go out and then repeats that cycle. The main burners ignite and the pilot stays on. I changed the pilot mechanism (with the igniter and sensor) and it still does the same thing. I've realized that the first time it turns on after being off a while it'll run for about a minute and then the off/on cycles get progressively more rapid until it just flicks on and shuts off. The filter is brand new and the blower comes on and works fine. It's just the burners keep turning off.

Update: I've tried to measure the resistance and voltage across all the meters and switches. All of them seemed to be functioning fine. However then I decided to bypass them all one by one, and the thermostat too, just to for a test. I know to never operate the furnace with any safety switch disabled. Anyway, I found that when I got to bypassing the pressure switch (model #PPS10008-2172) the furnace ran fine. Nothing is blocked and the furnace ignites fine. However last winter some of my vent were closed. So I wonder if it could've caused the sensor to break?

Nice troubleshooting! Being that the furnace is ten years old it is very possible that the pressure switch went bad. A pressure switch is just a diaphram of thin rubber and it is capable of wearing. Can you take an AMP draw reading off the inducer (exhaust) motor? I would like to see that before recommending a replacement pressure switch. Thank you.