Car wouldn't start so I started pulling the glow plugs. Imagine my surprise when I pulled the no. 1 glow plug and the glow plug tip didn't pull out with the rest of the glow plug. Now, I'm worried that if I stick something in there to try to fish it out, i'll push it further inside the cylinder. What do do now???

Might be difficult consider the block is iron, but they do make magnetic tipped extractors. I would get one to try and pull it out.

That's most likely your problem there. I wrote up this little tidbit on cold starting that's useful once you have your glow plugs fixed.

Since you pulled one that was falling apart, I would get 5 new plugs and replace them all. They're cheap enough for the insurance.

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If your glow plug light is turning on when you start the car, there's a high probability your plugs are working alright.

There's absolutely no need to take glow plugs out of the car to test them. Get a multimeter and follow this guide https://dieselgiant.com/glowplugrepair.htm.

Once you've checked that out, do the following:

1. Check your glow plugs, glow plug relay fuse, and battery health
2. Oil change to 5w40 weight oil with new filter.
3. Perform a valve adjustment -> very very important if you haven't done this recently.

That order will restore your cold starting ability. If it doesn't, I would seriously question the health of the motor.

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-Typos courtesy of my mobile phone.