Well, that's hard to say without looking at the unit in question, but the old rule applies..you need 3 things to fire a two stroke: Spark, compression and fuel mixture.
Spark should be easy to confirm...check for the correct mfg recommended spark plug. Just cuz it fits the hole and looks right doesn't mean it's the correct heat range. Once you have the right plug, lay the plug against the head for a good ground and crank it over with the plug out a few times, look for a consistent, bright blue spark. If it's yellow and/or intermittent, that's a weak spark....caused by bad plug, dirty points or some other electrical issue. If there's no spark, you really have a problem, of course.
If there's spark, what does the plug look like? If it's wet, black and sooty, it may be running rich. If it's whitish grey, it may be running lean. It should be, on a two stroke, about the color of charcoal or a little lighter, and not jet-black-wet.
It might be flooding out. In which case, pull the plug, pull the motor over a few times to clear the combustion chamber, dry off the plug and put it back in, and don't choke it. Another trick on flooded two strokes is to hold throttle wide open, no choke, and pull until it sputters to life.
The carb could be set way out of whack. Simple as two strokes are, once they start, they'll probably run, though maybe not well. Hard starting usually...*usually* is a carburetion issue...too much gas in the air/fuel mixture or not enough.
Maybe you just want to 'cheat' a little and start right out by pulling the plug and 'priming' it with a blast of WD-40 (assuming they havent' changed the formulation and it's still flammable, it works as a not-so-volatile starting fluid)
Like I've said, they're tempermental beasts, each with it's own personality. A person almost has to develop a relationship with each two stroke engine and learn it's tricks and quirks.
The easiest thing to do is to leave it home and crank by hand, or set yourself up with a cordless drill rig. Of course, again, that's if you're not chasing crappies all over by drilling 50 holes thru 3 feet of ice, but rather punching maybe a dozen 6 inch holes in a foot or less of ice, more if you have a fancy drill.
I go fishing because it's relaxing. Fighting with stubborn, heavy, tempermental engines doesn't fit the bill for relaxing in my book.