Last night I was able to diagnose and repair the Polaris snowmobile and have the owner come and collect it.
I threw a compression gauge on it even though my gut was telling me I could feel the two cylinders having compression and sure enough, both cylinders had relatively close compression.
After now confirming it had both spark and compression, the only other element to verify is fuel. I disconnected the fuel inlet line and threw my pressure gauge on it. It showed it was holding pressure which told me that the fuel level must be correct to close off the inlet needle.
From there I thought I would remove the PTO side carburetor and check to see if I had a broken reed or something in the intake. As I removed the carburetor it "felt" a bit light so I held it upright so as to not lose any fuel and brough it to the bench and removed the float bowl. Shockingly, when I removed the float bowl I discovered the bowl was empty.

If there was no fuel, why would the inlet needle be holding pressure with no fuel level to hold the float up? Also, I noticed that when I removed the fuel line from the carb to hook up the pressure pump, very, very little fuel came out, which that SHOULD have been the first red flag looking back.
I reconnected my pressure gauge and even with no float bowl on the carb, it held pressure. OK, that's not right. I removed the float pivot, float and needle from the seat and that's when I noticed the needle was stuck in the brass seat. I hit it with a little air and a piece of debris popped out. Hmmmm. So I went back to the sled and pulled the engine over a few times and a little trickle of fuel came out of the fuel line. I quickly removed the fuel line from the MAG side and it had fuel there bubbling up out of the line and when I pulled the engine over it spurted fuel out of the hose. Well, well, well, looks like we have a fuel delivery issue.

Could be a failing fuel pump, but I have not seen one fail before on only one chamber.
I went and removed the constant tension clamp from the fuel pump side of the PTO fuel line, then pulled the hose off the barb.
I used a little compressed air to blow backwards through the line from the carb side to the fuel pump side and blew into a paper towel. This was the result.
Not wanting to have a repeat issue, I removed the line from the other carb and did the same procedure as well as from the tank and ensured good clean fuel was flowing. Evidently letting a sled sit in a barn for a few years with no fuel in it is not a good practice.
With fuel supply now verified, I reinstalled the PTO side carb, reconnected everything and with the air box still removed I choked and gave her a couple of pulls. As soon as it fired off the tone was evident that she's now firing on both cylinders with excellent throttle response. Problem solved and the owner can come and get it.
Funny story time. I had opened the gate for the owner to back up to the shop to hook up to his trailer. My son, DIL and grandson were planning on stopping by for a visit and evidently when they pulled into the neighborhood, my grandson saw the lights on in the shop and said "Papas in the shop". So they pulled around back to the shop and when my son and grandson came into the shop my grandson wanted to sit on the snowmobile. My son was going over the various components with him and he knew the key and fuel tank and what to pull on to start it, so my son asked him if he wanted to see it run. Now I have to keep reminding myself that my grandson is not even 3-years old yet because he talks so clearly and surprises me every time I see him with his vocabulary as well as his imagination and the way his little mind works. My son pulled the handle and it fired right up, my grandson didn't even hesitate as he reached for and grabbed full throttle.

WOW! That happened fast.

The thing revved and track spun on the trailer and he didn't even flinch. My son grabbed his son's hand off the throttle and as we were laughing he explained to my grandson *********** the engine with the kill switch so he reached over and smacked the red killswitch then just sat there looking at the two of us. My hell, that kid has no fear and I'm not sure how I feel about that.
As they headed in the house the owner arrived and we had to let the shop air out a bit while he was hooking up the trailer. Sounds like he and his wife are going back up to their cabin this weekend, so he was pleased I was able to get it running so quickly for him. Nice to have that job out of the shop.
Thanks for looking.