If the following conditions are true:

1. Your "external machine" truly does have an open-collector output, and that transistor is working normally

2. The emitter of that same transistor is connected to ground

3. You have a 10kΩ resistance between collector and +3.3V

4. The only other thing connected to the collector is a working XOR gate input

then you absolutely should have a collector potential that goes between almost-ground (about 0.1V) and +3.3V.

So if you don't see those two possible conditions, then one of the above things is false.

With the collector potential clamped to a maximum of 0.6V, I suspect input protection diodes of the XOR gate are clamping the signal to ground. That would happen if the power supply (Vdd/Vcc) to the 74'86 IC is 0V, or broken or intermittent. Check that the Vdd/Vcc pin of the XOR IC is at least +3V.

If the following conditions are true:

1. Your "external machine" truly does have an open-collector output, and that transistor is working normally

2. The emitter of that same transistor is connected to ground

3. You have a 10kΩ resistance between collector and +3.3V

4. The only other thing connected to the collector is a working XOR gate input

then you absolutely should have a collector potential that goes between almost-ground (about 0.1V) and +3.3V.

So if you don't see those two possible conditions, then one of the above things is false.

With the collector potential clamped to a maximum of 0.6V, I suspect input protection diodes of the XOR gate are clamping the signal to ground. That would happen if the power supply (Vdd/Vcc) to the 74'86 IC is 0V, or broken or intermittent. Check that the Vdd/Vcc pin of the XOR IC is at least +3V.

A rise time of 3s is what would happen if R2 were not there. Check that it really is 10kΩ, and that it's properly connected at both ends.

Something that both these symptoms have in common is the +3.3V supply, so that's where I would check first. The slow rise time would suggest that the supply is physically disconnected, not just at 0V.