Can you confirm the model number of the transaxle by finding the Hydro Gear I.D. decal on the tranny.
I have had no luck finding a Hydro Gear manual for 351-0510.
I have a manual for 310-0510 and I do believe the 351is similar to it but I'm not certain the 310 manual can sub for the 351.
From your photo and your text, I'm not sure which spring you are calling "wrong". I have edited your photo to include numbers for positive ID of the spring. Pick one of them.
Also, did you perform the purge procedure after you changed the oil?

Mownie,

Thanks, I have attached a picture of the sticker that is stuck to the tranny.
The spring I was talking about is #2. When I have the brake pedal all the way back (in the maximum release position) the left end of the spring is loose in the hole that the hook goes through. I'm assuming this is because the metal plate is is hooked into is pushed all the way up against the bolt (dead center of picture) so can't go any further.

Purge procedure....no. I didn't know there was one.

I've since read that in some trannys there is a splined shaft that can get ground away. I'm reasonably mechincally minded but my fear was that if I undo the bolts holding the casing together, when I separate the two pieces things will just fall out and I won't know how to put them back again. Will things fall out if I do this or is everything attached inside ?
Also, on the parts diagram I have on Sears website there is no part number covering the brake system in my picture - any ideas what those part numbers are ?

Thanks

OK, let's do some basic checks before making any premature decisions to bust the case open. Because you stated that you are unaware of the need to purge air from the hydro, it is possible that your entire problem might be caused by the "FREE WHEELING LEVER" having somehow gotten partially activated.
This lever is what must be enabled when you need to move the tractor by "hand" when the engine is not running.
So, if you also are unaware of this feature, learn about it before doing anything else.
Do you have the Craftsman owner's manual for this tractor?
If so, there are 2 topics you need to read immediately.
The first topic, "TO TRANSPORT", explains the operation of the free wheeling lever (which operates the bypass valve, bypass valve lever is what spring #3 connects to in your pic).
The second topic to learn about is the purging procedure (a few pages after the free wheeling text).

I just got confirmation that the manual for "310-0510" covers all trans versions listed as -0510.
It is a free download if you go to the Hydro Gear website.
Beware there are 2 "options" regarding how the transaxle controls are configured (by the end user, aka Craftsman).
The tractor you have is configured with the "Friction Pack" option instead of the otherwise popular "Return To Neutral" option.
Keep that in mind when looking at the manual.
Behind the lever held on with the castellated nut is the brake caliper assembly. That lever has 2 "ramp like" cams which push in on 2 "Brake actuating pins" (items #62 in IPL).
Often in service, these pins will become gummed up or rusted in place and can cause the brake pucks to drag, sometimes dragging badly enough to keep the tractor from moving at all.
Find those pins and spray them with your favorite brand of rust bust product (aka Liquid Wrench, PB Blaster, etc.) to ensure that no dragging is happening.

Thanks. I tried earlier to reply but something went wrong and it didn't post so if you see two similar posts you'll know why.

I know what the freewheel lever is if you mean the lever I pull out that enables me to push the tractor around by hand. I will check to make sure it is all the way back in. There is a good amount of resistance when I try to set it to freewheel and it snaps back in place when I unhook it so I assume it's working properly.

As for the bypass valve being open in the purge procedure...does that mean the freewheel lever is in the "freewheel" position when I try to purge the air ?
Wheels off the ground, run in forward, then in reverse, 6 times each, then again with the valve closed ?
How is the air purged, through the expansion tank ?

Will - let me re-emphasize what Mownie mentioned earlier in this thread - you need to get your hands on an owner's manual for that machine; read and follow the maintenance advisories.
It will have detailed hydro tranny purging instructions, etc.....

Yes, the air will vent out through an atmospheric vent located in the expansion tank.
It behooves you to obtain the manuals from Sears and Hydro Gear if you have not done so, but yes, it is the free wheeling lever that operates the bypass valve when you are purging the tranny.

I have the owners manual and followed the instructions to purge the tranny. However, the tractor still makes a lot of noise when in gear and still doesn't pull very well up hills. Maybe a little better than before.
What could be causing the noise now, still air in the tranny perhaps ? Something else like a worn gear ?

Does the free wheeling (bypass) valve operate smoothly in & out when you perform the purge, or if you are doing it to roll the tractor by hand?
If the bypass valve does not move freely, and "click" into its proper detent positions.......it could be still bypassing a small volume of oil.
As to "worn gears" being the source of noise AND ALSO being related to poor performance: Highly unlikely. The gears in this unit are the few that are required for just ONE reduction ratio between the drive motor and the differential section of the unit, and the differential gears themselves.
The final reduction gearing would only be noisy during periods where the tractor ground speed was pretty fast and the pitch of the noise would change with any increase or decrease of ground speed.
The differential gears themselves DO NOT have any relative motion to each other EXCEPT when executing corners (turning tractor to left or right) or when one wheel is spinning due to a loss of traction. At all other times the differential gears may as well be welded together as they remain stationary relative to each other.

I suggest you might want to completely disassemble all the brake and friction pack parts for inspection, cleaning and lubing (where needed). Because Hydro Gear does list brake adjustment disorder as a possible cause of noise and poor performance, I am inclined to think that there may still be something about that friction pack and the brake caliper/pucks that may be at the root of the problem.
If you put the trans into free wheel mode, are you able to roll the tractor at all by hand? If not....that may be confirmation of a dragging brake.
If you undertake the disassembly of the brake and friction pack, be sure you take plenty of photos as you take it apart so you will know without question where each part came from and how it was oriented. Don't rely on the other manuals for that, they can sometimes be vague, but your own photos will be clear.

That pivot point has to be lubricated on a regular bassis or it wont fully engage the drive belt. Mine has whined since I bought it in 2006 the only other drive problem I have had is trying to use a aftermarket belt that did not fit properly. The original belt was streched.

This is just a long shot. For years I could not get the brake to activate on my tractor. Each spring I would fuss with it, but could not get brakes. When we moved into a yard with slopes, the brake became a necessity.

I found that there are channel in the frame and there were brake parts in that channel. Grass had become lodged in that channel and prevented the brake from working. This grass was not easily visible with an under tractor inspection.

Is there some place on your tractor where there could be debris interfering with the operation of the transmission? Some where that on cursory inspection that you would not see the debris?