Outdoor Power Equipment and Small Engines - Burnt something up on my riding tractor

I have an MTD Yard Machine with a 17.5 HP Briggs engine.
Model 13an607h352 Serial 1l050h10230 As soon as I tried to engage the blades the engine would stop. I saw a male connector with red and white wires hanging down along side my engine. Close by was a female connector with yellow and red wires. I hooked them together. When I tried to start the engine I saw a wisp of smoke come from the grill on top the engine. I guess I burnt something up because the engine doesn't even try to start now. Afterward I saw another female connector with red and white wires farther up along side the engine. Apparently I hooked the wrong connectors together. What do I need to fix my tractor?
Thank you!!

An update.....I found a fuse that was blown, replaced it and now at least the engine cranks but I am getting no spark. Do you have any idea what to replace?
Thank you!!

Yep, you probably put power to the kill wire on the coil and cooked the coil. You'll need a new one if so.

Thank you, cheese. How difficult is it to replace the coil?

Not hard at all. Just remove the engine shroud from the top of the engine and remove the old coil. Install the new one, rotate the engine so that the magnet pulls the coil to the flywheel, insert a .010" feeler guage (or a business card will work) between the coil and the magnets on the flywheel and tighten the coil bolts. Make sure to reconnect the small black wire to the coil too.