A3 Transmission Problems: 3rd, 4th, 5th Gear Not Working?

I'm currently having a frustrating problem with my A3, manufactured in 3/1997. The engine code is AGR and the transmission code is CZL.

Yesterday, I was driving a bit faster at a traffic light. When I shifted from second to third gear, there was a loud noise, and the gear slipped out of engagement.
I was then able to drive into a parking space, where I discovered that the reverse gear and the 1st and 2nd gears worked, but the 3rd, 4th, and 5th gears did not. The technician from the roadside assistance service said that the shaft attached to the transmission was likely broken.
He also shifted into a gear with his hands, and it appeared to be the 4th gear, based on the position of the gear knob, and then he suddenly experienced engine braking.
It's strange, but when I put it in 5th gear and release the clutch, you can hear a whirring sound coming from the transmission. That shouldn't be happening if I hadn't actually engaged a gear.
Is there any known defect where all three gears fail?
I've also adjusted Rainer's gearbox settings before.
I tried, but these three attempts didn't achieve anything.

Thank you in advance for your answers!

Hello,
Here's a translation:

"Just a guess - if your transmission has an external linkage system similar to the cable-operated gear selector on the Golf 1 (back then), the technician from the roadside assistance service might be able to shift gears by using a lever on the "shift shaft" at the transmission. If that's the case, you should be able to do it too."
You can see the positions for gears R, 1, and 2 on the transmission when you shift the gears using the gear lever. It's likely that for gears 3, 4, and 5, the shaft is extended or retracted further, and the external linkage no longer connects to it.
You might hear noises in gear position 5 because, after shifting into 5th gear, there is still some residual movement in the shifting mechanism within the transmission.
But again, that's just my assumption, without knowing your specific transmission.
Sure, here is the translation of the text from German to English:

"vg"

This is a common abbreviation for "very good" in German. It is often used in online forums and chat rooms.
Herbert.

His transmission has cable-operated shifting. It's a TDI engine installed transversely.

Hi,
Shouldn't it also be able to shift gears?
hg
Herbert.

Thank you for your responses!

Of course, it has cable controls.
I meant that switch thing with the metal weight on it.

Unfortunately, it seems like there is actual damage.
I removed the cover from the gearbox, and you can see that the 5th gear engages properly and has a solid connection when you select it using the gear knob. However, the wheels spin freely without any resistance.
I'm already looking for a new transmission. There are quite a few DQY models available on the market.
It should be a fairly direct translation, just a bit longer.

Please definitely include pictures if you know what caused the damage.

I will definitely do that.
I've never seen such damage before where three courses are unavailable, but the others are still working.
And I can't even sell my gearbox with the long 5th gear anyway, since it's broken.
so, it will be dissected .
As I mentioned, I have a cheap DQY available from an ASV.
I think it's slightly longer than the CZL.
Does anyone know if this will work? I think it should, though.

Just checked:
http://www.dieselschrauber.de/audi_zuord.html
DQY fits perfectly!
It's great that www.dieselschrauber.de exists.

Wouldn't this be the perfect opportunity to upgrade to a 6-speed transmission?

I've been thinking about that too.
However, I would then also convert the system to use VTG chargers, like Donalexo did. And actually, I've been wanting to sell the A3 for a while now.
Has anyone already converted it to a 6-speed transmission?
I think I'll also need the drive shafts.

... different flywheel, clutch, engine mount, possibly a different cable-operated gear system!

That's the reason why I extended the range of gears 3 through 5 on my transmission.

Yes, I've seen the pictures of your disassembled gearbox.
It's really impressive that you managed to fix it again.
And you even found a longer 5th one than I did .

I'm not familiar with your engine. I needed drive shafts, a starter, a clutch, and hydraulics for converting it to a DRW (Dual Rear Wheel) transmission.

Hi,

Quote:

I removed the cover from the gearbox, and you can see that the 5th gear engages properly and has a strong connection when you select it using the gear knob.

However, the wheels can spin freely. }
What do you mean by "locking" and "positive engagement"? If the gear wheel of 5th gear were locked with the synchronizer of 5th gear, the drive shaft and the output shaft would be clearly connected. If you then turn a wheel on a vehicle that is jacked up, the other wheel will rotate in the opposite direction via the differential. If the other wheel is blocked, the engine is also blocked, and you cannot turn it (otherwise, there would be a break in the differential or the output shaft). However, a break can be ruled out, since the transmission works in 1st and 2nd gear. Therefore, 5th gear was not engaged.
Either the shifting mechanism for gears 3, 4, and 5 in the transmission housing isn't working, or the colleague from the roadside assistance service was right that the external linkage is defective.
It's certainly possible that the corresponding levers/shift forks are also defective at the same time. However, I would first check this by attempting to shift directly at the shift shaft on the transmission housing. I described above how to determine the positions for 1st, 2nd, and reverse gears.
IMHO, the colleague from the roadside assistance service is right; by the way, he also managed to get it into 4th gear (= attempted to shift into 4th gear).
Sure, here is the translation of the text from German to English:

"vg"

This is a common abbreviation for "very good" in German. It is often used in online forums and chat rooms.
Herbert.

PS: I knew that the transmission was mounted transversely. Therefore, the movement at the gear lever needs to be "redirected by 90 degrees," so to speak. In some A3 transmissions, this is done with cable linkages, while in others it's done with levers and connecting rods (similar to the Golf 1). The key point is that you can shift directly from above, right next to the transmission.

Thank you, Herbert.
I understand how the transmission works.
My problem is that I don't have a positive end-of-life (EOL) condition in gears 3, 4, and 5.
That's why it's also logical that if the fifth gear is engaged, you can turn the tires.
Precisely because something is broken.
You can see, feel, and hear that the 5th gear is engaged.
Ich vermute einen Bruch der Nebenwelle zwischen 2. und 3. Okay.
I'll be able to see more once I've disassembled the old transmission.

Oh yes, I have one more question.
Specifically, the DQY is listed with ZMS.
Will it fit my AGR exhaust without a catalytic converter?