here is a carb. rebuild guide to give you an idea of the level of difficulity:
http://www.shopsbt.com/pdfs/mikunisbn.pdf You can get the rebuild kit for around $50 or less, but you need one for each carb. You can have a dealer do the carb rebuild, but as you can see from the guide it can be a little labor intensive, so most dealers will charge $100-$150 per carb. for labor..........it can get expensive unless you do it yourself. This really needs to be done every 3 or 4 years or your going to have trouble (probably more often if you run ethanol containing fuel).
The engine will run without the power valves working, but you loose a fair amount of top end power. The problem on the pre-2003 1200 series skis is that the valve could drop into a cylinder and do significant damage = need to rebuild the top end or the entire motor. The solution is called a wave-eater clip:
WaveEater Products So you need to find out if these or something similar has been installed on your power valves or not, and do the upgrade if needed.
I hate to add more bad news, but if that ski still has the catalytic converter, I'd look at getting rid of it as well and add a "D" plate. The cat/con is famous for failing after 10 years and causing more damage. Here is a site that has the clips and "D" plate:
http://www.islandracing.net/gp1200r.html
Unfortunately, you could be the poster child for "New Owner of a 2 Stroke Ski". I wish I had a dime for every post about someone that had just bought a 2 stroke ski, and was now having problems with it............I'd be rich.
I'd advise all new potential ski owners to only look at 4 stroke models............2 strokes are yesterdays technology, and buying a used one is a crap shoot.