Tecumseh 2 cycle snowblower engine: How much compression to run?

Most 2 cycles that I have worked on needs at least 100 psi to even try to run. Good normal compression is around 120 psi minimum.
 
Please be aware many Tecumseh parts are NLA since the Tecumseh original manufacture has been out of business since 2009. The group that took over the Tecumseh line only provides parts for the newer that they built after 2009.
 
Also 2 cycle equipment will wear both the rings and cylinder requiring a new oversized piston rings just like 4 cycle equipment. Now if this the 1500-1589A these are not available, only the standard sizes. With this in mind there is only a 50/50 chance that you simply need rings.
 
Either way you got to figure out which engine model you do have to even get the correct parts list lookup to see even if the parts you are wanting are available or not.

It is highly unlikely that a 2 stroke snow engine would be worn out, they normally don't get enough use. Poor quality oil or improper fuel mix are more common causes of failure. Remove the muffler and check for piston scoring and/or signs of excessive blowby.

I inherited this machine when I got married 13 years ago and it had been given to her by her Uncle who bought it at a yard sale.  It's been running strong for over 13 years now, but I did park it 3 years ago (and apparently never drained the gas, which is why I'm cleaning the carb).  I did take the exhaust off and looked at the piston.  It didn't look scored but it was dark (carbon deposit?).  
 
How exactly do you check blow by?
 
I'll try to finish the carb this weekend and try to start it...and let you know how it goes.  I'll also run another compression test this weekend too.

Carb kit installed (cleaned the carb and the kit came with a new diaphram), it fired up and ran after the gas reached the carb.  Took a bit to get it to warm up; typical as I recall.  The choke has two positions.  Initial start uses full choke for a cold start.  Once it warmed up, the engine would stall with choke off.  Runs and surges at partial choke, but when I place it under load of the auger ON, I can go with choke off and it runs good.  
 
I think it just needs a few tanks of gas run through it once we get some snow.