I have a 81 Yz 465 and I've been trying to help my dad get it started, he's had the bike for 30 years but only ever used it as a hill climb bike. 
Its been sitting for years and after tearing it down we found that the kicker gear was destroyed, and their is a hole is the clutch side of the case because of it. I bought a used but basically brand new kicker gear, installed it and then the new kicker wouldn't move at all. Turns out the new kicker gear gets stuck in the hole the old one made. 
My question is can you repair the whole in the case? Or maybe somehow start the bike electrically and avoid the kicker altoghether? My foot is bruised after trying to kick it over pretty much every time..
The bike has started multiple times with the beat up kicker gear, its not easy but it ran just like it did 20 years ago. 

Hopeful to get it fully running as my 72 year old dad wants to do a hill climb one last time. 

If possible pics of the damage would help give a reasonable answer. Pics have to be loaded from something like imgur or similar. Damage doesn't sound good though. I had a 465G new in "80 so same beast. Did I see your pics of the damage on another site or a Facebook thing. I dunno I'm 77 & get lost on the internet & can't find things second time around. Could tow start it with your car but it's all a bit dodgy if it goes wrong & tow rope has to pull from the centre then across to the left grip holding by hand to let go easy. Damn it ignore all that as sound dangerous even if I've done it many times haha.

Greetings from Tennessee  
  yes pictures upload on Imgur, google photos etc
just copy and paste 

imgur.com/a/d3haMBY

It’s not the best picture, but the damage is in the top left of the case. There is a hole through it into the other case, you can even see a gear through the hole. You can see another hole patched years ago with a blue resin but that isn’t the issue. I wish I had a better picture but won’t unless I get it out again soon.
 The new kicker gear has a tab that sheard off on the old one, and that is what is getting stuck in the hole and completely seizing the new gear.

 

imgur.com/a/d3haMBY

It’s not the best picture, but the damage is in the top left of the case. There is a hole through it into the other case, you can even see a gear through the hole. You can see another hole patched years ago with a blue resin but that isn’t the issue. I wish I had a better picture but won’t unless I get it out again soon.
The new kicker gear has a tab that sheard off on the old one, and that is what is getting stuck in the hole and completely seizing the new gear.
No I’m not the same guy as on Facebook. I don’t doubt this is a very common problem on these bikes though as this bike only has about 1000 total miles and the kicker is already completely destroyed 

photos.app.goo.gl/LUiZY83u85rKwiDY9
Just be sure when you assemble it that the kick gear friction clip bent ear is in the groove as makes the gear move out to engage.
They were hard on kick shaft stops too so look close at yours. Check the pics in my link.
Revolve the kick gears around each other as can bend teeth which eventualy break due to kick back although kickback can indicate a damaged flywheel woodruff key.
Bit hard to tell how bad the case damage is on my old computer but i tend to run with damage if possible but up to you. The blue stuff i guess is just stopping oil escape behind the shaft so just keep it bunged. Can't see the damage showing a gear looking through the damage. Only teeth i can see is first gear looking though a 'genuine hole' by the kick intermediate gear which is normal. But maybe i'm not looking in the right place.
Are you sure it's a YZ as they're a race bike only. In fact that's my one in my Avatar pic.
The IT465 is the trail & road version, so thought i'd ask as you say its done 1000 miles but whatever you're a lucky man.

I don't see the "broken" hole either? 

imgur.com/a/jtOH5dK

The highlighted spot is where the hole is.
I don’t currently have a better picture, I wasn’t really taking pictures as it was supposed to be an easy kicker gear swap but turned into something much worse.
It definitely is a Yz465, my dad extended the rear so he can hill climb with it easier. He hillclimbed for 30 years in just about anything Yamaha. His original hillclimber was a dt 400 but he’s even taken a it175 and easily made the hill.

imgur.com/a/jtOH5dK

Sorry I hope to get a better picture soon. The hole is in the circled part. There’s like a lip where the hole is that you can’t see.

I just expanded your pic up for a better look but not sure what to say.
Can't see directly into where you say the gear is visible.
But if the gear is catching on the damage can you just relieve the damage for the gear to pass by.
Other thought 'are you running the locating dowels' in the case as without them it could move enough to cause things to go tight to move--possibly.
Where the damage is its your decission to decide if the case is strong enough to support the shaft when under kicking pressure.
I tend to try & get away with damage if its not too bad.
Bottom line i guess is buy a new case which then becomes a major dismantle of course.