Where should I start looking for problems and what types of things could be wrong?

2001 Ford Ranger
4 cyl.
Manual Tran.
99,000 Miles

You should check the engine. So, yeah definitely start by checking the engine first.

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08 4.0 Sport 4x4
Stock

Get the codes read and bring 'em back here for us to take a gander at. Until then, we have no clue. Some auto parts stores will read them for you for free.

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Sgtsandman's Work in Progress
2011 Ranger XLT, 4X4, 4 door Super Cab. 4.0L, 5 Speed M50D-R1HD, 3.73:1, 8.8" open differential, Jason Pace cap
2019 Ford Ranger STX FX4, Super Crew, 2.3L Ecoboost, 10 speed automatic, 3.73:1 with rear locker, Leer 100XR cap

Keep in mind that how your engine runs, idles, and starts is still the primary indication of it's condition. A check engine light still needs to be addressed however since it allows you to spot a small problem before it becomes obvious.

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08 4.0 Sport 4x4
Stock

Absolutely nothing has changed as far as performance, starts perfectly. The light just came on right when I started up later in the day.

I'm so broke right now, so I think I'm just going to invest in a engine diagnostics tool for around $60

Very stupid question, but could this thing possibly come on if a windshield washer fluid cover fell off, I check under the hood and I guess it fell off... recently :/

Or you could put the $60 dollars toward whatever repair is necessary by getting your code read at an autozone. Or whatever national auto parts chain you got over there.
Then post 'em. Or if your reasonable confident in the recommendations of the counter guy doing the read, buy the part on the spot. And we'll help you understand how to change it. It's probably an oxygen sensor or some other emissions related thing like DPFE sensor etc.

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08 4.0 Sport 4x4
Stock

What Mickblock said. If you are tight on cash, use it for the repair. You can always get a code reader later.

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Sgtsandman's Work in Progress
2011 Ranger XLT, 4X4, 4 door Super Cab. 4.0L, 5 Speed M50D-R1HD, 3.73:1, 8.8" open differential, Jason Pace cap
2019 Ford Ranger STX FX4, Super Crew, 2.3L Ecoboost, 10 speed automatic, 3.73:1 with rear locker, Leer 100XR cap

I called an Autozone and they don't do that where I live

Autozone is supposed to read the codes for free... weird that they don't.

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05 Mitsubishi Lancer LS
17 Mazda CX-3
03 Ford Ranger XL - SOLD!
01 Honda Civic LX - SOLD!

Ya apparently they stopped doing that at auto parts stores in California 2 years ago.

Advance, O'Reily's, Murray's, Giant, Van Senus? Who ever. Call em all up! Just the franchises though.

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08 4.0 Sport 4x4
Stock

Oh it must be a California thing. The OBD (codes) system is primarily a system required by the California born federal emissions regulations.

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08 4.0 Sport 4x4
Stock

It's true.. autoparts stores won't read codes in CA anymore... CLICK

You might as well buy one. It'd be cheaper in the long run.

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05 Mitsubishi Lancer LS
17 Mazda CX-3
03 Ford Ranger XL - SOLD!
01 Honda Civic LX - SOLD!

I disconnected the battery and let sit for 5 minutes, the light went away, drove for a few minutes and it did not come back on yet, hopefully it won't be back...

I was pretty low on oil, I put a quart and a half in there and now its between MIN and MAX, perhaps that was the reason it came on?

wow thats really weird that just cali would stop it. i know its just a shot into space but my guess is your egr value. thats if it still runs the good (same as before) just my .02
good luck with gettin that fixed