I have a Toro 38182 (serial #260004679) snow blower (single stage) for which the pull start is very difficult (it pulls out but with much resistance).  I replaced the recoil starter, but that wasn't the issue.  The electric starts works fine.  The pull start works fine with the spark plug removed.  Could the issue be the flywheel (or the flywheel key - not sure what it's called in the parts diagram for this snowblower).  Should I remove the flywheel to look (is it easy to take off and put back on for this snow blower).  Could it be compression value related (how would I diagnose that).  Any suggestions are much appreciated.  
 
Thank you.

I'm not familiar with that machine however if the engine runs fine once started, there's nothing wrong with the flywheel / keyway  
 
 The gear on the outside of the flywheel for the electric start has to be good or it wouldn't spin it over. 
 
If you can post up what the engine is specifically, it can be checked (parts diagram) for a compression release located on the cam shaft.
 
Should that be the issue, pulling at least the side cover(RS) would be required to access the camshaft..

I do not believe this snow blower (single stage) has a cam shaft (just a crankshaft).  Parts 169 and 172 do refer to Compression Release.  Thank you.
 
[font="'helvetica neue', arial, helvetica, sans-serif; font-size: 22px"]ENGINE ASSEMBLY TECUMSEH HSK635 1723C Parts Diagram
 
 

This is a two-stroke engine.

The engine diagram was taken from partstree.com.
 
I tried (a couple of times) to post the link, but that was evidently deleted from the post.

Interesting....  
 
The compression release, looking at a parts pic, seems to be reed style valve:

 
The only thing I can think of is to check for any play in crankshaft, on both ends. Pull / push in all directions checking for any play.
A very long shot but possibly the flywheel is indeed hitting the coil if the engine has worn bearings..
 
Good thing is the electric start works...  I would make sure any part you may want to pull (gasket, etc) is still available. 
 
Please post back if you find the issue, good luck.
 
 

I’m leaning towards an issue with the compression release (cover), like you believe it is, but I haven’t removed that part yet.  It looks like I would need to remove the recoil starter first, then the Housing for the Blower to get at this part.  Once I remove this part (one screw, I believe), would it be as “simple” as merely replacing the compression release cover for another, or would I need to possibly do more.  I doubt it’s related to the flywheel since with the spark plug removed the pull start is fine.  


Since electric start does work, I’m hesitant to do more other than, possibly, a quick replacement of parts, which I can handle.
 
Thank you.

I'm not sure exactly how a "reed valve style" compression release works. 
 
The parts diagram indicates it's pretty easy to replace and there really isn't any other moving parts to fail/be the issue...
 
It certainly can't hurt to replace it and can only help... 
 
Please post back how it goes, if it goes, etc..

Ok, replaced the compression release cover (and gasket).  Not easy finding the part, but found it and easy to replace. That was not the issue.  I’m focused on cylinder exhaust ports, in particular cleaning under the cylinder head.  The cylinder head is secured with 5 torx screws, and very difficult to loosen (probably for good reason).  The snow blower does start (at least it did before I started taking things apart, but haven’t tried again), and may want to stop here.  would you suggest looking into removing this cylinder head to get at the cylinder exhaust ports and cleaning any carbon build-up?  It states in my manual that the exhaust and cylinder ports should be cleaned every 75-100 hours of operation.  I did clean the muffler exhaust port, but that was reasonably clean.  Also, i’m unsure if these torx screws are torqued.  Thanks.

I had a non start Poulan Pro blower (2 stroke) that indeed had the ring carboned up. 
Once cleaned, it starts / runs fine:
 

 
Recently, I had a weed eater that didn't want to start.  I set the engine at TDC and put Seafoam in the cylinder and let sit for a day.  It cranked up first pull the next day and still runs fine...
 
If you can look into the exhaust port and check the piston for any scoring would be helpful.  Checking compression, at least 100PSI would also help with diagnosis.   A peek down the cylinder with a bore scope/camera would also be helpful if possible...
 
Pulling the cylinder and cleaning the ring(s) isn't that hard.  Just make sure you have gaskets etc.  As for torque, good and snug with RED loctite has worked fine for me...  
 
I would check the above first (and Seafoam), before pulling the top end apart.  As it is an older engine, a new piston ring couldn't hurt..