The fact that it started "sounding sick" makes me believe the induction fan squirrel cage scattered, but there's no reason it'd cut the pilot unless it's tied into the millivoltage circuit as a failsafe.
Another thing that will make the old girl "sound sick" is that your flue could be blocked. Sometimes there's a flapper right where the flue exits the furnace. Pull the flue off, it's a matter of a couple screws. Suck all that crap out with a shop vac.
At that point, you gotta use your head. Does it look like noirmal precipitation, crust and rust, or are there pieces of pinecone and junk in there that shouldn't be there?
If the second is true, you probably have critters working in your flue and you need to take a look.
If your flue exits near the foundation and you guys have lots of snow, go shovel it out and make sure the snow and ice hasn't backed up the flue or created a plug or just piled against the flue. That'll solve the problem.
If a low pressure limit shut down the pilot circuit, you may need to correct the flue problem before the pilot will relight.
If this stuff doesn't work, suck it up and call the furnace guy. If you can run SAFE temporary heat until tomorrow, it'll be a lot cheaper. Furnaces are designed to break on Super Bowl Sunday. It's because no one is available to fix them, and if they are, they'll charge you an arm and a leg.
