Ok, so you redid the plug wire ends? On the coil you just spin off the collar around the end of the coil that the plug wire goes into, then you can remove the wire from the coil. The plug cap end just threads on, unless someone replaced it with something else in its lifetime.
If the plug is black, not sooty black as you didn't mention if its smoking at all, then its running rich which could be the bane of your problems as Cave Rider mentioned. My 200ES used to foul plugs constantly, but in my case it was due to the stock exhaust being rotted out and restricted inside. After replacing the exhaust it was actually running perfect, nice tan plug color, etc.
Try adjusting the mixture screw on the carb, screw it in all the way lightly seated and come back out about 1 1/2-2 turns, see if you can get it running again, might need to clean the plug good or even replace it. I usually clean then with a brass brush then some carb cleaner and let dry. That will usually bring a fouled plug back unless its got other issues. Also check the gap .24-.28 for the gap. I gap mine to .25 and it seems to be the sweet spot for mine.
If you get it running again after making those adjustments ride it around for a good 10-15 mins, vary engine speed, a few takeoffs, idling, etc.. Get the engine up to full temp and then after that playing around check the plug color again. If your still running rich, and the fact that your spark arrestor is stuck you might have an exhaust issue. If you don't need a spark arrestor for where you ride and you can't get that dang thing out the end of the pipe you could cut it off ahead of the bolt that holds the arrestor in, but i would work on it a bit more. Got a rubber mallet? Smack it all the way around the pipe a few times to loosen it up, soak it with some PB Blaster, drive it around again and get the exhaust warmed up to help with removal. If all that doesnt work do you have access to a torch? Might have to apply some good heat around the end of the pipe to crack it free.
I have seen those arrestors totally covered with a layer of carbon build up, choking the exhaust. I had one that run like crap and felt like it was held back at full throttle, got that arrestor out and revved it up and it was a cloud of crap coming out of the exhaust, left the arrestor out for a while and it ran good. The arrestor had to go into a fire for a while to burn it clean, no kidding!
It's frustrating ones like this i really wish i was close enough to just grab my tool bag and head over... LOL... I got a email from a forum member over on 3WO about a month ago and i ended up driving a couple hours to go help him on a weekend. He was about to rip his hair out. A fresh set of eyes and some beer and it was running like a top.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....
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. the needle is the pointy part at the end of your throttle cable, and the emulsion tube is the portion that it sets in, it is also what your main jet screws into... the tube can only come from Honda... back to the CDI box... if it has already been running, with the wiring you have done, and was running correctly, your problem probably does not lie there, unless the cheap CDI box failed. there are versions of the 
