I don't know anything about snow blowers, but if you post the model#'s, it may be helpful for someone else to assist you.
16"? Sounds kind of small for an 8 HP!

You're thinking right of the drive issue. on the starter- does it run but not engage? Or doesn't run at all? In either case, if you pull the starter you can inspect the drive for wear and that it moves freely on the shaft. If you need to lube it- do so sparingly as lube on the wrong parts of the gear will cause it to slip.You can also turn the starter shaft- that helps the brushes kind of re-seat themselves after sitting. Sometimes this helps them run again.

Sorry about that. It is a 26inch machine. The model # is 315E740F000.

The starter does nothing at all. I pulled it apart a few years ago and cleaned the armature. I found a parts list on ordertree.com

Go to-
http://www.m-and-d.com/parts.html
Click Illustrated parts diagrams online-
"" Click here for lookup
Select MTD on the menu, upper left
Scroll all the way down to Yardm.....
Snow throwers
2001

They list a 31AE740F000