Welcome to the nuthouse, you could not have found a better place to get you back on the road to GS happiness, this place is filled with good folk who know the GS like the back of thier hand, and you will not find more know how and folk wlling to help anywhere.
Basscliff will be along shortly to give you his world famous, mega welcome, that includes links to his site and more GS knowlage than you ever knew existed, he is scary.
Ok, no the stator is not needed to start or run the bike, as long as you have a good battery, the stator is there to charge the battery, not supply spark.
But I hate to be the bearer of bad tidings

, you said you changed the oil, I hope you put the correct oil into the engine, these motors are very sensitive to that and only take one specific type of oil, Agip, 5W-40 full synthetic, if you put any other oil in it, and even tried to turn it over, I am afraid, you have damaged not only the cylinder bores, but the crankshaft as well and the motor will not start or run.
The only way to remedy this is a complete strip down and rebuild, including new pistons, rings, crankshaft and all the gearbox gears and bearings.
Of little cheer though, is your drive shart should be fine, as you did not ride it, just tried to start it, you should be able to do the job yourself but it won't be cheap, 650 parts are not easy to come by and are expensive......................sorry
OK, relax and breath again, just yanking your chain, there is nothing wrong with your motor, I am sure it is just fine.:lol:
Can you give us a bit of history, when did the bike last run?
What fairy tales did the previos owner tell you....

When you say it won't start, what exactly does it do, crank over and not fire up, try to fire up, backfire, not crank at all....???
You do know about the clutch lock out switch, you need to pull the clutch lever in when starting.
Your motor needs a few things to run;
1 Spark
2 Compression
3 Fuel/air mixture
Check for spark first, pull a spark plug out, lay the ground electrode against the motor and crank it, you should get a fat blue spark.
I assume the compression is enough to start the bike, but no harm putting a compression tester on and checking, remember to hold the throttle wide open when you check. As a matter of course, adjust the valves.
Carbs need to be removed, and cleaned properly, stripped, dipped and new O-Rings fitted.
All the information on the above will be in Basscliffs welcome, so lets establish the above first and take it from there.
Don't sweat it, we will have you riding before you know it.
Oh yes, and
WE LIKE PICTURES